Auxiliary-field quantum Monte Carlo methods in nuclei
Alhassid, Y
2016-01-01
Auxiliary-field quantum Monte Carlo methods enable the calculation of thermal and ground state properties of correlated quantum many-body systems in model spaces that are many orders of magnitude larger than those that can be treated by conventional diagonalization methods. We review recent developments and applications of these methods in nuclei using the framework of the configuration-interaction shell model.
An Auxiliary-Field Quantum Monte Carlo Study of the Chromium Dimer
Purwanto, Wirawan; Zhang, Shiwei; Krakauer, Henry
2014-01-01
The chromium dimer (Cr2) presents an outstanding challenge for many-body electronic structure methods. Its complicated nature of binding, with a formal sextuple bond and an unusual potential energy curve, is emblematic of the competing tendencies and delicate balance found in many strongly correlated materials. We present a near-exact calculation of the potential energy curve (PEC) and ground state properties of Cr2, using the auxiliary-field quantum Monte Carlo (AFQMC) method. Unconstrained,...
Auxiliary-field quantum Monte Carlo calculations of the molybdenum dimer
Purwanto, Wirawan; Krakauer, Henry
2016-01-01
Chemical accuracy is difficult to achieve for systems with transition metal atoms. Third row transition metal atoms are particularly challenging due to strong electron-electron correlation in localized d-orbitals. The Cr2 molecule is an outstanding example, which we previously treated with highly accurate auxiliary-field quantum Monte Carlo (AFQMC) calculations [Purwanto et al., J. Chem. Phys. 142, 064302 (2015)]. Somewhat surprisingly, computational description of the isoelectronic Mo2 dimer has also, to date, been scattered and less than satisfactory. We present high-level theoretical benchmarks of the Mo2 singlet ground state ($X ^1\\Sigma_g^+$) and first triplet excited state ($a ^3\\Sigma_u^+$), using the phaseless AFQMC calculations. Extrapolation to the complete basis set limit is performed. Excellent agreement with experimental spectroscopic constants is obtained. We also present a comparison of the correlation effects in Cr2 and Mo2.
An auxiliary-field quantum Monte Carlo study of the chromium dimer
Energy Technology Data Exchange (ETDEWEB)
Purwanto, Wirawan, E-mail: wirawan0@gmail.com; Zhang, Shiwei; Krakauer, Henry [Department of Physics, College of William and Mary, Williamsburg, Virginia 23187-8795 (United States)
2015-02-14
The chromium dimer (Cr{sub 2}) presents an outstanding challenge for many-body electronic structure methods. Its complicated nature of binding, with a formal sextuple bond and an unusual potential energy curve (PEC), is emblematic of the competing tendencies and delicate balance found in many strongly correlated materials. We present an accurate calculation of the PEC and ground state properties of Cr{sub 2}, using the auxiliary-field quantum Monte Carlo (AFQMC) method. Unconstrained, exact AFQMC calculations are first carried out for a medium-sized but realistic basis set. Elimination of the remaining finite-basis errors and extrapolation to the complete basis set limit are then achieved with a combination of phaseless and exact AFQMC calculations. Final results for the PEC and spectroscopic constants are in excellent agreement with experiment.
An Auxiliary-Field Quantum Monte Carlo Study of the Chromium Dimer
Purwanto, Wirawan; Krakauer, Henry
2014-01-01
The chromium dimer (Cr2) presents an outstanding challenge for many-body electronic structure methods. Its complicated nature of binding, with a formal sextuple bond and an unusual potential energy curve, is emblematic of the competing tendencies and delicate balance found in many strongly correlated materials. We present a near-exact calculation of the potential energy curve (PEC) and ground state properties of Cr2, using the auxiliary-field quantum Monte Carlo (AFQMC) method. Unconstrained, exact AFQMC calculations are first carried out for a medium-sized but realistic basis set. Elimination of the remaining finite-basis errors and extrapolation to the complete basis set (CBS) limit is then achieved with a combination of phaseless and exact AFQMC calculations. Final results for the PEC and spectroscopic constants are in excellent agreement with experiment.
Auxiliary-Field Quantum Monte Carlo Simulations of Neutron Matter in Chiral Effective Field Theory
Wlazłowski, G; Moroz, S; Bulgac, A; Roche, K J
2014-01-01
We present variational Monte Carlo calculations of the neutron matter equation of state using chiral nuclear interactions. The ground-state wavefunction of neutron matter, containing non-perturbative many-body correlations, is obtained from auxiliary-field quantum Monte Carlo simulations of up to about 340 neutrons interacting on a 10^3 discretized lattice. The evolution Hamiltonian is chosen to be attractive and spin-independent in order to avoid the fermion sign problem and is constructed to best reproduce broad features of chiral nuclear forces. This is facilitated by choosing a lattice spacing of 1.5 fm, corresponding to a momentum-space cutoff of 414 MeV/c, a resolution scale at which strongly repulsive features of nuclear two-body forces are suppressed. Differences between the evolution potential and the full chiral nuclear interaction are then treated perturbatively. Our results for the equation of state are compared to previous quantum Monte Carlo simulations which employed chiral two-body forces at n...
Purwanto, Wirawan; Al-Saidi, W. A.; Krakauer, Henry; Zhang, Shiwei
2007-01-01
The use of an approximate reference state wave function |Phi_r> in electronic many-body methods can break the spin symmetry of Born-Oppenheimer spin-independent Hamiltonians. This can result in significant errors, especially when bonds are stretched or broken. A simple spin-projection method is introduced for auxiliary-field quantum Monte Carlo (AFQMC) calculations, which yields spin-contamination-free results, even with a spin-contaminated |Phi_r>. The method is applied to the difficult F2 m...
Auxiliary-field quantum Monte Carlo study of first- and second-row post-d elements
Al-Saidi, W A; Zhang, S; Krakauer, Henry; Zhang, Shiwei
2006-01-01
A series of calculations for the first- and second-row post-d elements (Ga-Br and In-I) are presented using the phaseless auxiliary-field quantum Monte Carlo (AF QMC) method. This method is formulated in a Hilbert space defined by any chosen one-particle basis, and maps the many-body problem into a linear combination of independent-particle solutions with external auxiliary fields. The phase/sign problem is handled approximately by the phaseless formalism using a trial wave function, which in our calculations was chosen to be the Hartree-Fock solution. We used the consistent correlated basis sets of Peterson and coworkers, which employ a small core relativistic pseudopotential. The AF QMC results are compared with experiment and with those from density-functional (GGA and B3LYP) and coupled-cluster CCSD(T) calculations. The AF QMC total energies agree with CCSD(T) to within a few milli-hartrees across the systems and over several basis sets. The calculated atomic electron affinities, ionization energies, and ...
Qin, Mingpu; Zhang, Shiwei
2016-01-01
Ground state properties of the Hubbard model on a two-dimensional square lattice are studied by the auxiliary-field quantum Monte Carlo method. Accurate results for energy, double occupancy, effective hopping, magnetization, and momentum distribution are calculated for interaction strengths of U/t from 2 to 8, for a range of densities including half-filling and n = 0.3, 0.5, 0.6, 0.75, and 0.875. At half-filling, the results are numerically exact. Away from half-filling, the constrained path Monte Carlo method is employed to control the sign problem. Our results are obtained with several advances in the computational algorithm, which are described in detail. We discuss the advantages of generalized Hartree-Fock trial wave functions and its connection to pairing wave functions, as well as the interplay with different forms of Hubbard-Stratonovich decompositions. We study the use of different twist angle sets when applying the twist averaged boundary conditions. We propose the use of quasi-random sequences, whi...
Purwanto, Wirawan; Zhang, Shiwei; Krakauer, Henry
2008-01-01
We show that the recently developed phaseless auxiliary-field quantum Monte Carlo (AFQMC) method can be used to study excited states, providing an alternative to standard quantum chemistry methods. The phaseless AFQMC approach, whose computational cost scales as M^3-M^4 with system size M, has been shown to be among the most accurate many-body methods in ground state calculations. For excited states, prevention of collapse into the ground state and control of the Fermion sign/phase problem ar...
Stabilizing Canonical-Ensemble Calculations in the Auxiliary-Field Monte Carlo Method
Gilbreth, C N
2014-01-01
Quantum Monte Carlo methods are powerful techniques for studying strongly interacting Fermi systems. However, implementing these methods on computers with finite-precision arithmetic requires careful attention to numerical stability. In the auxiliary-field Monte Carlo (AFMC) method, low-temperature or large-model-space calculations require numerically stabilized matrix multiplication. When adapting methods used in the grand-canonical ensemble to the canonical ensemble of fixed particle number, the numerical stabilization increases the number of required floating-point operations for computing observables by a factor of the size of the single-particle model space, and thus can greatly limit the systems that can be studied. We describe an improved method for stabilizing canonical-ensemble calculations in AFMC that exhibits better scaling, and present numerical tests that demonstrate the accuracy and improved performance of the method.
Auxiliary field Monte-Carlo study of the QCD phase diagram at strong coupling
Ohnishi, Akira; Nakano, Takashi Z
2012-01-01
We investigate the QCD phase diagram in the strong coupling limit by using a newly developed auxiliary field Monte-Carlo (AFMC) method. Starting from an effective action in the leading order of the 1/g^2 and 1/d expansion with one species of unrooted staggered fermion, we solve the many-body problem exactly by introducing the auxiliary fields and integrating out the temporal links and quark fields. We have a sign problem in AFMC, which is different from the original one in finite density lattice QCD. For low momentum auxiliary field modes, a complex phase cancellation mechanism exists, and the sign problem is not serious on a small lattice. Compared with the mean field results, the transition temperature is found to be reduced by around 10 % and the hadron phase is found to be extended in the larger chemical potential direction by around 20 %, as observed in the monomer-dimer-polymer (MDP) simulations.
Monte Carlo Simulation of Quantum Computation
Cerf, N. J.; Koonin, S. E.
1997-01-01
The many-body dynamics of a quantum computer can be reduced to the time evolution of non-interacting quantum bits in auxiliary fields by use of the Hubbard-Stratonovich representation of two-bit quantum gates in terms of one-bit gates. This makes it possible to perform the stochastic simulation of a quantum algorithm, based on the Monte Carlo evaluation of an integral of dimension polynomial in the number of quantum bits. As an example, the simulation of the quantum circuit for the Fast Fouri...
Projector quantum Monte Carlo with matrix product states
Wouters, Sebastian; Verstichel, Brecht; Van Neck, Dimitri; Chan, Garnet Kin-Lic
2014-01-01
We marry tensor network states (TNS) and projector quantum Monte Carlo (PMC) to overcome the high computational scaling of TNS and the sign problem of PMC. Using TNS as trial wave functions provides a route to systematically improve the sign structure and to eliminate the bias in fixed-node and constrained-path PMC. As a specific example, we describe phaseless auxiliary-field quantum Monte Carlo with matrix product states (MPS-AFQMC). MPS-AFQMC improves significantly on the density-matrix ren...
Quantum Gibbs ensemble Monte Carlo
International Nuclear Information System (INIS)
We present a path integral Monte Carlo method which is the full quantum analogue of the Gibbs ensemble Monte Carlo method of Panagiotopoulos to study the gas-liquid coexistence line of a classical fluid. Unlike previous extensions of Gibbs ensemble Monte Carlo to include quantum effects, our scheme is viable even for systems with strong quantum delocalization in the degenerate regime of temperature. This is demonstrated by an illustrative application to the gas-superfluid transition of 4He in two dimensions
Quantum Monte Carlo diagonalization method as a variational calculation
Energy Technology Data Exchange (ETDEWEB)
Mizusaki, Takahiro; Otsuka, Takaharu [Tokyo Univ. (Japan). Dept. of Physics; Honma, Michio
1997-05-01
A stochastic method for performing large-scale shell model calculations is presented, which utilizes the auxiliary field Monte Carlo technique and diagonalization method. This method overcomes the limitation of the conventional shell model diagonalization and can extremely widen the feasibility of shell model calculations with realistic interactions for spectroscopic study of nuclear structure. (author)
MontePython: Implementing Quantum Monte Carlo using Python
J.K. Nilsen
2006-01-01
We present a cross-language C++/Python program for simulations of quantum mechanical systems with the use of Quantum Monte Carlo (QMC) methods. We describe a system for which to apply QMC, the algorithms of variational Monte Carlo and diffusion Monte Carlo and we describe how to implement theses methods in pure C++ and C++/Python. Furthermore we check the efficiency of the implementations in serial and parallel cases to show that the overhead using Python can be negligible.
New Massive Supergravity and Auxiliary Fields
Bergshoeff, Eric A; Parra, Lorena; Rosseel, Jan; Yin, Yihao; Zojer, Thomas
2013-01-01
We construct a supersymmetric formulation of linearized New Massive Gravity without introducing higher derivatives. Instead, we introduce supersymmetrically a set of bosonic and fermionic auxiliary fields which, upon elimination by their equations of motion, introduce fourth-order derivative terms for the metric and third-order derivative terms for the gravitino. Our construction requires an off-shell formulation of the three-dimensional supersymmetric massive Fierz--Pauli theory. We discuss the non-linear extension of our results.
Quantum Monte Carlo calculations of neutron matter with chiral three-body forces
Tews, I.; Gandolfi, S.; Gezerlis, A.; Schwenk, A.
2016-02-01
Chiral effective field theory (EFT) enables a systematic description of low-energy hadronic interactions with controlled theoretical uncertainties. For strongly interacting systems, quantum Monte Carlo (QMC) methods provide some of the most accurate solutions, but they require as input local potentials. We have recently constructed local chiral nucleon-nucleon (NN) interactions up to next-to-next-to-leading order (N2LO ). Chiral EFT naturally predicts consistent many-body forces. In this paper, we consider the leading chiral three-nucleon (3N) interactions in local form. These are included in auxiliary field diffusion Monte Carlo (AFDMC) simulations. We present results for the equation of state of neutron matter and for the energies and radii of neutron drops. In particular, we study the regulator dependence at the Hartree-Fock level and in AFDMC and find that present local regulators lead to less repulsion from 3N forces compared to the usual nonlocal regulators.
Quantum Monte Carlo calculations of two neutrons in finite volume
Klos, P.; Lynn, J. E.; Tews, I.; Gandolfi, S.; Gezerlis, A.; Hammer, H. -W.; Hoferichter, M.; Schwenk, A.
2016-01-01
Ab initio calculations provide direct access to the properties of pure neutron systems that are challenging to study experimentally. In addition to their importance for fundamental physics, their properties are required as input for effective field theories of the strong interaction. In this work, we perform auxiliary-field diffusion Monte Carlo calculations of the ground and first excited state of two neutrons in a finite box, considering a simple contact potential as well as chiral effectiv...
Brane worlds in gravity with auxiliary fields
International Nuclear Information System (INIS)
Recently, Pani et al. explored a new theory of gravity by adding nondynamical fields, i.e., gravity with auxiliary fields (Phys Rev D 88:121502, 2013). In this gravity theory, higher-order derivatives of matter fields generically appear in the field equations. In this paper we extend this theory to any dimensions and discuss the thick braneworld model in five dimensions. Domain wall solutions are obtained numerically. The stability of the brane system under tensor perturbations is analyzed. We find that the system is stable under tensor perturbations and the gravity zero mode is localized on the brane. Therefore, the four-dimensional Newtonian potential can be realized on the brane. (orig.)
Brane worlds in gravity with auxiliary fields
Energy Technology Data Exchange (ETDEWEB)
Guo, Bin; Liu, Yu-Xiao; Yang, Ke [Lanzhou University, Institute of Theoretical Physics, Lanzhou (China)
2015-02-01
Recently, Pani et al. explored a new theory of gravity by adding nondynamical fields, i.e., gravity with auxiliary fields (Phys Rev D 88:121502, 2013). In this gravity theory, higher-order derivatives of matter fields generically appear in the field equations. In this paper we extend this theory to any dimensions and discuss the thick braneworld model in five dimensions. Domain wall solutions are obtained numerically. The stability of the brane system under tensor perturbations is analyzed. We find that the system is stable under tensor perturbations and the gravity zero mode is localized on the brane. Therefore, the four-dimensional Newtonian potential can be realized on the brane. (orig.)
Frontiers of quantum Monte Carlo workshop: preface
International Nuclear Information System (INIS)
The introductory remarks, table of contents, and list of attendees are presented from the proceedings of the conference, Frontiers of Quantum Monte Carlo, which appeared in the Journal of Statistical Physics
Quantum Monte Carlo calculations with chiral effective field theory interactions
International Nuclear Information System (INIS)
The neutron-matter equation of state connects several physical systems over a wide density range, from cold atomic gases in the unitary limit at low densities, to neutron-rich nuclei at intermediate densities, up to neutron stars which reach supranuclear densities in their core. An accurate description of the neutron-matter equation of state is therefore crucial to describe these systems. To calculate the neutron-matter equation of state reliably, precise many-body methods in combination with a systematic theory for nuclear forces are needed. Chiral effective field theory (EFT) is such a theory. It provides a systematic framework for the description of low-energy hadronic interactions and enables calculations with controlled theoretical uncertainties. Chiral EFT makes use of a momentum-space expansion of nuclear forces based on the symmetries of Quantum Chromodynamics, which is the fundamental theory of strong interactions. In chiral EFT, the description of nuclear forces can be systematically improved by going to higher orders in the chiral expansion. On the other hand, continuum Quantum Monte Carlo (QMC) methods are among the most precise many-body methods available to study strongly interacting systems at finite densities. They treat the Schroedinger equation as a diffusion equation in imaginary time and project out the ground-state wave function of the system starting from a trial wave function by propagating the system in imaginary time. To perform this propagation, continuum QMC methods require as input local interactions. However, chiral EFT, which is naturally formulated in momentum space, contains several sources of nonlocality. In this Thesis, we show how to construct local chiral two-nucleon (NN) and three-nucleon (3N) interactions and discuss results of first QMC calculations for pure neutron systems. We have performed systematic auxiliary-field diffusion Monte Carlo (AFDMC) calculations for neutron matter using local chiral NN interactions. By
Quantum Monte Carlo calculations with chiral effective field theory interactions
Energy Technology Data Exchange (ETDEWEB)
Tews, Ingo
2015-10-12
The neutron-matter equation of state connects several physical systems over a wide density range, from cold atomic gases in the unitary limit at low densities, to neutron-rich nuclei at intermediate densities, up to neutron stars which reach supranuclear densities in their core. An accurate description of the neutron-matter equation of state is therefore crucial to describe these systems. To calculate the neutron-matter equation of state reliably, precise many-body methods in combination with a systematic theory for nuclear forces are needed. Chiral effective field theory (EFT) is such a theory. It provides a systematic framework for the description of low-energy hadronic interactions and enables calculations with controlled theoretical uncertainties. Chiral EFT makes use of a momentum-space expansion of nuclear forces based on the symmetries of Quantum Chromodynamics, which is the fundamental theory of strong interactions. In chiral EFT, the description of nuclear forces can be systematically improved by going to higher orders in the chiral expansion. On the other hand, continuum Quantum Monte Carlo (QMC) methods are among the most precise many-body methods available to study strongly interacting systems at finite densities. They treat the Schroedinger equation as a diffusion equation in imaginary time and project out the ground-state wave function of the system starting from a trial wave function by propagating the system in imaginary time. To perform this propagation, continuum QMC methods require as input local interactions. However, chiral EFT, which is naturally formulated in momentum space, contains several sources of nonlocality. In this Thesis, we show how to construct local chiral two-nucleon (NN) and three-nucleon (3N) interactions and discuss results of first QMC calculations for pure neutron systems. We have performed systematic auxiliary-field diffusion Monte Carlo (AFDMC) calculations for neutron matter using local chiral NN interactions. By
Fast quantum Monte Carlo on a GPU
Lutsyshyn, Y
2013-01-01
We present a scheme for the parallelization of quantum Monte Carlo on graphical processing units, focusing on bosonic systems and variational Monte Carlo. We use asynchronous execution schemes with shared memory persistence, and obtain an excellent acceleration. Comparing with single core execution, GPU-accelerated code runs over x100 faster. The CUDA code is provided along with the package that is necessary to execute variational Monte Carlo for a system representing liquid helium-4. The program was benchmarked on several models of Nvidia GPU, including Fermi GTX560 and M2090, and the latest Kepler architecture K20 GPU. Kepler-specific optimization is discussed.
Interaction picture density matrix quantum Monte Carlo
International Nuclear Information System (INIS)
The recently developed density matrix quantum Monte Carlo (DMQMC) algorithm stochastically samples the N-body thermal density matrix and hence provides access to exact properties of many-particle quantum systems at arbitrary temperatures. We demonstrate that moving to the interaction picture provides substantial benefits when applying DMQMC to interacting fermions. In this first study, we focus on a system of much recent interest: the uniform electron gas in the warm dense regime. The basis set incompleteness error at finite temperature is investigated and extrapolated via a simple Monte Carlo sampling procedure. Finally, we provide benchmark calculations for a four-electron system, comparing our results to previous work where possible
New braneworld models in the presence of auxiliary fields
Bazeia, D; Menezes, R; Moreira, D C
2014-01-01
We study braneworld models in the presence of auxiliary fields. We use the first-order framework to investigate several distinct possibilities, where the standard braneworld scenario changes under the presence of the parameter that controls the auxiliary fields introduced to modify Einstein's equation. The results add to previous ones, to show that the minimal modification that we investigate contributes to change quantitatively the thick braneworld profile, although no new qualitative effect is capable of being induced by the minimal modification here considered.
Monte Carlo methods in AB initio quantum chemistry quantum Monte Carlo for molecules
Lester, William A; Reynolds, PJ
1994-01-01
This book presents the basic theory and application of the Monte Carlo method to the electronic structure of atoms and molecules. It assumes no previous knowledge of the subject, only a knowledge of molecular quantum mechanics at the first-year graduate level. A working knowledge of traditional ab initio quantum chemistry is helpful, but not essential.Some distinguishing features of this book are: Clear exposition of the basic theory at a level to facilitate independent study. Discussion of the various versions of the theory: diffusion Monte Carlo, Green's function Monte Carlo, and release n
Quantum Monte Carlo calculations of light nuclei
International Nuclear Information System (INIS)
Quantum Monte Carlo calculations using realistic two- and three-nucleon interactions are presented for nuclei with up to eight nucleons. We have computed the ground and a few excited states of all such nuclei with Greens function Monte Carlo (GFMC) and all of the experimentally known excited states using variational Monte Carlo (VMC). The GFMC calculations show that for a given Hamiltonian, the VMC calculations of excitation spectra are reliable, but the VMC ground-state energies are significantly above the exact values. We find that the Hamiltonian we are using (which was developed based on 3H, 4He, and nuclear matter calculations) underpredicts the binding energy of p-shell nuclei. However our results for excitation spectra are very good and one can see both shell-model and collective spectra resulting from fundamental many-nucleon calculations. Possible improvements in the three-nucleon potential are also be discussed
Quantum Monte Carlo with Variable Spins
Melton, Cody A; Mitas, Lubos
2016-01-01
We investigate the inclusion of variable spins in electronic structure quantum Monte Carlo, with a focus on diffusion Monte Carlo with Hamiltonians that include spin-orbit interactions. Following our previous introduction of fixed-phase spin-orbit diffusion Monte Carlo (FPSODMC), we thoroughly discuss the details of the method and elaborate upon its technicalities. We present a proof for an upper-bound property for complex nonlocal operators, which allows for the implementation of T-moves to ensure the variational property. We discuss the time step biases associated with our particular choice of spin representation. Applications of the method are also presented for atomic and molecular systems. We calculate the binding energies and geometry of the PbH and Sn$_2$ molecules, as well as the electron affinities of the 6$p$ row elements in close agreement with experiments.
No-compromise reptation quantum Monte Carlo
International Nuclear Information System (INIS)
Since its publication, the reptation quantum Monte Carlo algorithm of Baroni and Moroni (1999 Phys. Rev. Lett. 82 4745) has been applied to several important problems in physics, but its mathematical foundations are not well understood. We show that their algorithm is not of typical Metropolis-Hastings type, and we specify conditions required for the generated Markov chain to be stationary and to converge to the intended distribution. The time-step bias may add up, and in many applications it is only the middle of a reptile that is the most important. Therefore, we propose an alternative, 'no-compromise reptation quantum Monte Carlo' to stabilize the middle of the reptile. (fast track communication)
Discovering correlated fermions using quantum Monte Carlo.
Wagner, Lucas K; Ceperley, David M
2016-09-01
It has become increasingly feasible to use quantum Monte Carlo (QMC) methods to study correlated fermion systems for realistic Hamiltonians. We give a summary of these techniques targeted at researchers in the field of correlated electrons, focusing on the fundamentals, capabilities, and current status of this technique. The QMC methods often offer the highest accuracy solutions available for systems in the continuum, and, since they address the many-body problem directly, the simulations can be analyzed to obtain insight into the nature of correlated quantum behavior. PMID:27518859
Discovering correlated fermions using quantum Monte Carlo
Wagner, Lucas K.; Ceperley, David M.
2016-09-01
It has become increasingly feasible to use quantum Monte Carlo (QMC) methods to study correlated fermion systems for realistic Hamiltonians. We give a summary of these techniques targeted at researchers in the field of correlated electrons, focusing on the fundamentals, capabilities, and current status of this technique. The QMC methods often offer the highest accuracy solutions available for systems in the continuum, and, since they address the many-body problem directly, the simulations can be analyzed to obtain insight into the nature of correlated quantum behavior.
Energy Technology Data Exchange (ETDEWEB)
Wu, Congjun; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-01-15
Quantum Monte-Carlo (QMC) simulations involving fermions have the notorious sign problem. Some well-known exceptions of the auxiliary field QMC algorithm rely on the factorizibility of the fermion determinant. Recently, a fermionic QMC algorithm has been found in which the fermion determinant may not necessarily factorizable, but can instead be expressed as a product of complex conjugate pairs of eigenvalues, thus eliminating the sign problem for a much wider class of models. In this paper, we present general conditions for the applicability of this algorithm and point out that it is deeply related to the time reversal symmetry of the fermion matrix. We apply this method to various models of strongly correlated systems at all doping levels and lattice geometries, and show that many novel phases can be simulated without the sign problem.
Quantum Monte Carlo Simulations : Algorithms, Limitations and Applications
Raedt, H. De
1992-01-01
A survey is given of Quantum Monte Carlo methods currently used to simulate quantum lattice models. The formalisms employed to construct the simulation algorithms are sketched. The origin of fundamental (minus sign) problems which limit the applicability of the Quantum Monte Carlo approach is shown
Quantum Monte Carlo for vibrating molecules
International Nuclear Information System (INIS)
Quantum Monte Carlo (QMC) has successfully computed the total electronic energies of atoms and molecules. The main goal of this work is to use correlation function quantum Monte Carlo (CFQMC) to compute the vibrational state energies of molecules given a potential energy surface (PES). In CFQMC, an ensemble of random walkers simulate the diffusion and branching processes of the imaginary-time time dependent Schroedinger equation in order to evaluate the matrix elements. The program QMCVIB was written to perform multi-state VMC and CFQMC calculations and employed for several calculations of the H2O and C3 vibrational states, using 7 PES's, 3 trial wavefunction forms, two methods of non-linear basis function parameter optimization, and on both serial and parallel computers. In order to construct accurate trial wavefunctions different wavefunctions forms were required for H2O and C3. In order to construct accurate trial wavefunctions for C3, the non-linear parameters were optimized with respect to the sum of the energies of several low-lying vibrational states. In order to stabilize the statistical error estimates for C3 the Monte Carlo data was collected into blocks. Accurate vibrational state energies were computed using both serial and parallel QMCVIB programs. Comparison of vibrational state energies computed from the three C3 PES's suggested that a non-linear equilibrium geometry PES is the most accurate and that discrete potential representations may be used to conveniently determine vibrational state energies
Quantum Monte Carlo calculations for carbon nanotubes
Luu, Thomas; Lähde, Timo A.
2016-04-01
We show how lattice quantum Monte Carlo can be applied to the electronic properties of carbon nanotubes in the presence of strong electron-electron correlations. We employ the path-integral formalism and use methods developed within the lattice QCD community for our numerical work. Our lattice Hamiltonian is closely related to the hexagonal Hubbard model augmented by a long-range electron-electron interaction. We apply our method to the single-quasiparticle spectrum of the (3,3) armchair nanotube configuration, and consider the effects of strong electron-electron correlations. Our approach is equally applicable to other nanotubes, as well as to other carbon nanostructures. We benchmark our Monte Carlo calculations against the two- and four-site Hubbard models, where a direct numerical solution is feasible.
Quantum Monte Carlo calculations of two neutrons in finite volume
Klos, P; Tews, I; Gandolfi, S; Gezerlis, A; Hammer, H -W; Hoferichter, M; Schwenk, A
2016-01-01
Ab initio calculations provide direct access to the properties of pure neutron systems that are challenging to study experimentally. In addition to their importance for fundamental physics, their properties are required as input for effective field theories of the strong interaction. In this work, we perform auxiliary-field diffusion Monte Carlo calculations of the ground and first excited state of two neutrons in a finite box, considering a simple contact potential as well as chiral effective field theory interactions. We compare the results against exact diagonalizations and present a detailed analysis of the finite-volume effects, whose understanding is crucial for determining observables from the calculated energies. Using the L\\"uscher formula, we extract the low-energy S-wave scattering parameters from ground- and excited-state energies for different box sizes.
Quantum Monte Carlo for vibrating molecules
Energy Technology Data Exchange (ETDEWEB)
Brown, W.R. [Univ. of California, Berkeley, CA (United States). Chemistry Dept.]|[Lawrence Berkeley National Lab., CA (United States). Chemical Sciences Div.
1996-08-01
Quantum Monte Carlo (QMC) has successfully computed the total electronic energies of atoms and molecules. The main goal of this work is to use correlation function quantum Monte Carlo (CFQMC) to compute the vibrational state energies of molecules given a potential energy surface (PES). In CFQMC, an ensemble of random walkers simulate the diffusion and branching processes of the imaginary-time time dependent Schroedinger equation in order to evaluate the matrix elements. The program QMCVIB was written to perform multi-state VMC and CFQMC calculations and employed for several calculations of the H{sub 2}O and C{sub 3} vibrational states, using 7 PES`s, 3 trial wavefunction forms, two methods of non-linear basis function parameter optimization, and on both serial and parallel computers. In order to construct accurate trial wavefunctions different wavefunctions forms were required for H{sub 2}O and C{sub 3}. In order to construct accurate trial wavefunctions for C{sub 3}, the non-linear parameters were optimized with respect to the sum of the energies of several low-lying vibrational states. In order to stabilize the statistical error estimates for C{sub 3} the Monte Carlo data was collected into blocks. Accurate vibrational state energies were computed using both serial and parallel QMCVIB programs. Comparison of vibrational state energies computed from the three C{sub 3} PES`s suggested that a non-linear equilibrium geometry PES is the most accurate and that discrete potential representations may be used to conveniently determine vibrational state energies.
Measuring Berry curvature with quantum Monte Carlo
Kolodrubetz, Michael
2014-01-01
The Berry curvature and its descendant, the Berry phase, play an important role in quantum mechanics. They can be used to understand the Aharonov-Bohm effect, define topological Chern numbers, and generally to investigate the geometric properties of a quantum ground state manifold. While Berry curvature has been well-studied in the regimes of few-body physics and non-interacting particles, its use in the regime of strong interactions is hindered by the lack of numerical methods to solve it. In this paper we fill this gap by implementing a quantum Monte Carlo method to solve for the Berry curvature, based on interpreting Berry curvature as a leading correction to imaginary time ramps. We demonstrate our algorithm using the transverse-field Ising model in one and two dimensions, the latter of which is non-integrable. Despite the fact that the Berry curvature gives information about the phase of the wave function, we show that our algorithm has no sign or phase problem for standard sign-problem-free Hamiltonians...
Quantum Monte Carlo methods algorithms for lattice models
Gubernatis, James; Werner, Philipp
2016-01-01
Featuring detailed explanations of the major algorithms used in quantum Monte Carlo simulations, this is the first textbook of its kind to provide a pedagogical overview of the field and its applications. The book provides a comprehensive introduction to the Monte Carlo method, its use, and its foundations, and examines algorithms for the simulation of quantum many-body lattice problems at finite and zero temperature. These algorithms include continuous-time loop and cluster algorithms for quantum spins, determinant methods for simulating fermions, power methods for computing ground and excited states, and the variational Monte Carlo method. Also discussed are continuous-time algorithms for quantum impurity models and their use within dynamical mean-field theory, along with algorithms for analytically continuing imaginary-time quantum Monte Carlo data. The parallelization of Monte Carlo simulations is also addressed. This is an essential resource for graduate students, teachers, and researchers interested in ...
Quantum Monte Carlo Endstation for Petascale Computing
Energy Technology Data Exchange (ETDEWEB)
Lubos Mitas
2011-01-26
NCSU research group has been focused on accomplising the key goals of this initiative: establishing new generation of quantum Monte Carlo (QMC) computational tools as a part of Endstation petaflop initiative for use at the DOE ORNL computational facilities and for use by computational electronic structure community at large; carrying out high accuracy quantum Monte Carlo demonstration projects in application of these tools to the forefront electronic structure problems in molecular and solid systems; expanding the impact of QMC methods and approaches; explaining and enhancing the impact of these advanced computational approaches. In particular, we have developed quantum Monte Carlo code (QWalk, www.qwalk.org) which was significantly expanded and optimized using funds from this support and at present became an actively used tool in the petascale regime by ORNL researchers and beyond. These developments have been built upon efforts undertaken by the PI's group and collaborators over the period of the last decade. The code was optimized and tested extensively on a number of parallel architectures including petaflop ORNL Jaguar machine. We have developed and redesigned a number of code modules such as evaluation of wave functions and orbitals, calculations of pfaffians and introduction of backflow coordinates together with overall organization of the code and random walker distribution over multicore architectures. We have addressed several bottlenecks such as load balancing and verified efficiency and accuracy of the calculations with the other groups of the Endstation team. The QWalk package contains about 50,000 lines of high quality object-oriented C++ and includes also interfaces to data files from other conventional electronic structure codes such as Gamess, Gaussian, Crystal and others. This grant supported PI for one month during summers, a full-time postdoc and partially three graduate students over the period of the grant duration, it has resulted in 13
Auxiliary Field Meson Model at Finite Temperature and Density
Kouno, H; Kashiwa, K; Hamada, M; Tokudome, H; Matsuzaki, M; Yahiro, M
2005-01-01
Starting from many quark interactions, we construct a nonlinear sigma-omega model at finite temperature and density. The mesons are introduced as auxiliary fields. Effective quark-meson couplings are strongly related to effective meson masses, since they are derived simultaneously from the original many quark interactions. In this model, even if the effective omega-meson mass decreases due to the partial chiral restoration, the equation of state (EOS) of nuclear matter can become soft.
Auxiliary field formulation of supersymmetric nonlinear sigma models
International Nuclear Information System (INIS)
Two dimensional N=2 supersymmetric nonlinear sigma models on hermitian symmetric spaces are formulated in terms of the auxiliary superfields. If we eliminate auxiliary vector and chiral superfields, they give D- and F- term constraints to define the target manifolds. The integration over auxiliary vector superfields, which can be performed exactly, is equivalent to the elimination of the auxiliary fields by the use of the classical equations of motion. (author)
Hybrid algorithms in quantum Monte Carlo
International Nuclear Information System (INIS)
With advances in algorithms and growing computing powers, quantum Monte Carlo (QMC) methods have become a leading contender for high accuracy calculations for the electronic structure of realistic systems. The performance gain on recent HPC systems is largely driven by increasing parallelism: the number of compute cores of a SMP and the number of SMPs have been going up, as the Top500 list attests. However, the available memory as well as the communication and memory bandwidth per element has not kept pace with the increasing parallelism. This severely limits the applicability of QMC and the problem size it can handle. OpenMP/MPI hybrid programming provides applications with simple but effective solutions to overcome efficiency and scalability bottlenecks on large-scale clusters based on multi/many-core SMPs. We discuss the design and implementation of hybrid methods in QMCPACK and analyze its performance on current HPC platforms characterized by various memory and communication hierarchies.
Quantum Monte Carlo for atoms and molecules
International Nuclear Information System (INIS)
The diffusion quantum Monte Carlo with fixed nodes (QMC) approach has been employed in studying energy-eigenstates for 1--4 electron systems. Previous work employing the diffusion QMC technique yielded energies of high quality for H2, LiH, Li2, and H2O. Here, the range of calculations with this new approach has been extended to include additional first-row atoms and molecules. In addition, improvements in the previously computed fixed-node energies of LiH, Li2, and H2O have been obtained using more accurate trial functions. All computations were performed within, but are not limited to, the Born-Oppenheimer approximation. In our computations, the effects of variation of Monte Carlo parameters on the QMC solution of the Schroedinger equation were studied extensively. These parameters include the time step, renormalization time and nodal structure. These studies have been very useful in determining which choices of such parameters will yield accurate QMC energies most efficiently. Generally, very accurate energies (90--100% of the correlation energy is obtained) have been computed with single-determinant trail functions multiplied by simple correlation functions. Improvements in accuracy should be readily obtained using more complex trial functions
Formulation and Application of Quantum Monte Carlo Method to Fractional Quantum Hall Systems
Suzuki, Sei; Nakajima, Tatsuya
2003-01-01
Quantum Monte Carlo method is applied to fractional quantum Hall systems. The use of the linear programming method enables us to avoid the negative-sign problem in the Quantum Monte Carlo calculations. The formulation of this method and the technique for avoiding the sign problem are described. Some numerical results on static physical quantities are also reported.
Instantons in Quantum Annealing: Thermally Assisted Tunneling Vs Quantum Monte Carlo Simulations
Jiang, Zhang; Smelyanskiy, Vadim N.; Boixo, Sergio; Isakov, Sergei V.; Neven, Hartmut; Mazzola, Guglielmo; Troyer, Matthias
2015-01-01
Recent numerical result (arXiv:1512.02206) from Google suggested that the D-Wave quantum annealer may have an asymptotic speed-up than simulated annealing, however, the asymptotic advantage disappears when it is compared to quantum Monte Carlo (a classical algorithm despite its name). We show analytically that the asymptotic scaling of quantum tunneling is exactly the same as the escape rate in quantum Monte Carlo for a class of problems. Thus, the Google result might be explained in our framework. We also found that the transition state in quantum Monte Carlo corresponds to the instanton solution in quantum tunneling problems, which is observed in numerical simulations.
Bispinor Auxiliary Fields in Duality-Invariant Electrodynamics Revisited
Ivanov, E. A.; Zupnik, B. M.
2012-01-01
Motivated by a recent progress in studying the duality-symmetric models of nonlinear electrodynamics, we revert to the auxiliary tensorial (bispinor) field formulation of the O(2) duality proposed by us in arXiv:hep-th/0110074, arXiv:hep-th/0303192. In this approach, the entire information about the given duality-symmetric system is encoded in the O(2) invariant interaction Lagrangian which is a function of the auxiliary fields V_{\\alpha\\beta}, \\bar V_{\\dot \\alpha\\dot \\beta}. We extend this s...
Linear Scaling Quantum Monte Carlo Calculations
Williamson, Andrew
2002-03-01
New developments to the quantum Monte Carlo approach are presented that improve the scaling of the time required to calculate the total energy of a configuration of electronic coordinates from N^3 to nearly linear[1]. The first factor of N is achieved by applying a unitary transform to the set of single particle orbitals used to construct the Slater determinant, creating a set of maximally localized Wannier orbitals. These localized functions are then truncated beyond a given cutoff radius to introduce sparsity into the Slater determinant. The second factor of N is achieved by evaluating the maximally localized Wannier orbitals on a cubic spline grid, which removes the size dependence of the basis set (e.g. plane waves, Gaussians) typically used to expand the orbitals. Application of this method to the calculation of the binding energy of carbon fullerenes and silicon nanostructures will be presented. An extension of the approach to deal with excited states of systems will also be presented in the context of the calculation of the excitonic gap of a variety of systems. This work was performed under the auspices of the U.S. Dept. of Energy at the University of California/LLNL under contract no. W-7405-Eng-48. [1] A.J. Williamson, R.Q. Hood and J.C. Grossman, Phys. Rev. Lett. 87 246406 (2001)
Monte Carlo Hamiltonian: Generalization to Quantum Field Theory
Luo, Xiang-Qian; Jirari, H.; Kroger, H; Moriarty, K.
2001-01-01
Monte Carlo techniques with importance sampling have been extensively applied to lattice gauge theory in the Lagrangian formulation. Unfortunately, it is extremely difficult to compute the excited states using the conventional Monte Carlo algorithm. Our recently developed approach: the Monte Carlo Hamiltonian method, has been designed to overcome the difficulties of the conventional approach. In this paper, we extend the method to many body systems and quantum field theory. The Klein-Gordon f...
Excited states and transition metal compounds with quantum Monte Carlo
Bande, Annika
2007-01-01
To the most challenging electron structure calculations belong weak interactions, excited state calculations, transition metals and properties. In this work the performance of variational (VMC) and fixed-node diffusion quantum Monte Carlo (FN-DMC) is tested for challenging electron structure problems using the quantum Monte Carlo amolqc code by Lüchow et al. The transition metal compounds under consideration are vanadium oxides. Here excitation, ionization, oxygen atom and molecule abstractio...
Monte Carlo simulation of quantum Zeno effect in the brain
Georgiev, Danko
2014-01-01
Environmental decoherence appears to be the biggest obstacle for successful construction of quantum mind theories. Nevertheless, the quantum physicist Henry Stapp promoted the view that the mind could utilize quantum Zeno effect to influence brain dynamics and that the efficacy of such mental efforts would not be undermined by environmental decoherence of the brain. To address the physical plausibility of Stapp's claim, we modeled the brain using quantum tunneling of an electron in a multiple-well structure such as the voltage sensor in neuronal ion channels and performed Monte Carlo simulations of quantum Zeno effect exerted by the mind upon the brain in the presence or absence of environmental decoherence. The simulations unambiguously showed that the quantum Zeno effect breaks down for timescales greater than the brain decoherence time. To generalize the Monte Carlo simulation results for any n-level quantum system, we further analyzed the change of brain entropy due to the mind probing actions and proved ...
Qin, Mingpu; Zhang, Shiwei
2016-01-01
The vast majority of quantum Monte Carlo (QMC) calculations in interacting fermion systems require a constraint to control the sign problem. The constraint involves an input trial wave function which restricts the random walks. We introduce a systematically improvable constraint which relies on the fundamental role of the density or one-body density matrix. An independent-particle calculation is coupled to an auxiliary-field QMC calculation. The independent-particle solution is used as the constraint in QMC, which then produces the input density or density matrix for the next iteration. The constraint is optimized by the self-consistency between the many-body and independent-particle calculations. The approach is demonstrated in the two-dimensional Hubbard model by accurately determining the spin densities when collective modes separated by tiny energy scales are present in the magnetic and charge correlations. Our approach also provides an ab initio way to predict effective "U" parameters for independent-par...
Parent formulations, frame-like Lagrangians, and generalized auxiliary fields
Grigoriev, Maxim
2012-01-01
We elaborate on the recently proposed Lagrangian parent formulation. In particular, we identify a natural choice of the allowed field configurations ensuring the equivalence of the parent and the starting point Lagrangians. We also analyze the structure of the generalized auxiliary fields employed in the parent formulation and establish the relationship between the parent Lagrangian and the recently proposed Lagrange structure for the unfolded dynamics. As an illustration of the parent formalism a systematic derivation of the frame-like Lagrangian for totally symmetric fields starting from the Fronsdal one is given. We also present a concise and manifestly sp(2)-symmetric form of the off-shell constraints and gauge symmetries for AdS space symmetric fields at the nonlinear level.
Optimum and efficient sampling for variational quantum Monte Carlo
Trail, John Robert; 10.1063/1.3488651
2010-01-01
Quantum mechanics for many-body systems may be reduced to the evaluation of integrals in 3N dimensions using Monte-Carlo, providing the Quantum Monte Carlo ab initio methods. Here we limit ourselves to expectation values for trial wavefunctions, that is to Variational quantum Monte Carlo. Almost all previous implementations employ samples distributed as the physical probability density of the trial wavefunction, and assume the Central Limit Theorem to be valid. In this paper we provide an analysis of random error in estimation and optimisation that leads naturally to new sampling strategies with improved computational and statistical properties. A rigorous lower limit to the random error is derived, and an efficient sampling strategy presented that significantly increases computational efficiency. In addition the infinite variance heavy tailed random errors of optimum parameters in conventional methods are replaced with a Normal random error, strengthening the theoretical basis of optimisation. The method is ...
Quantum Monte Carlo with Coupled-Cluster wave functions
Roggero, Alessandro; Mukherjee, Abhishek; Pederiva, Francesco
2013-01-01
We introduce a novel many body method which combines two powerful many body techniques, viz., quantum Monte Carlo and coupled cluster theory. Coupled cluster wave functions are introduced as importance functions in a Monte Carlo method designed for the configuration interaction framework to provide rigorous upper bounds to the ground state energy. We benchmark our method on the homogeneous electron gas in momentum space. The importance function used is the coupled cluster doubles wave functio...
Quantum Monte Carlo approaches to nuclear and atomic physics
Carlson, J.; Gandolfi, Stefano; Gezerlis, Alexandros
2012-01-01
Quantum Monte Carlo methods have proven to be valuable in the study of strongly correlated quantum systems, particularly nuclear physics and cold atomic gases. Historically, such ab initio simulations have been used to study properties of light nuclei, including spectra and form factors, low-energy scattering, and high-momentum properties including inclusive scattering and one- and two-body momentum distributions. More recently they have been used to study the properties of homogeneous and in...
Monte Carlo simulation of quantum Zeno effect in the brain
Georgiev, Danko
2015-12-01
Environmental decoherence appears to be the biggest obstacle for successful construction of quantum mind theories. Nevertheless, the quantum physicist Henry Stapp promoted the view that the mind could utilize quantum Zeno effect to influence brain dynamics and that the efficacy of such mental efforts would not be undermined by environmental decoherence of the brain. To address the physical plausibility of Stapp's claim, we modeled the brain using quantum tunneling of an electron in a multiple-well structure such as the voltage sensor in neuronal ion channels and performed Monte Carlo simulations of quantum Zeno effect exerted by the mind upon the brain in the presence or absence of environmental decoherence. The simulations unambiguously showed that the quantum Zeno effect breaks down for timescales greater than the brain decoherence time. To generalize the Monte Carlo simulation results for any n-level quantum system, we further analyzed the change of brain entropy due to the mind probing actions and proved a theorem according to which local projections cannot decrease the von Neumann entropy of the unconditional brain density matrix. The latter theorem establishes that Stapp's model is physically implausible but leaves a door open for future development of quantum mind theories provided the brain has a decoherence-free subspace.
Quantum Monte Carlo simulation with a black hole
Benić, Sanjin; Yamamoto, Arata
2016-05-01
We perform quantum Monte Carlo simulations in the background of a classical black hole. The lattice discretized path integral is numerically calculated in the Schwarzschild metric and in its approximated metric. We study spontaneous symmetry breaking of a real scalar field theory. We observe inhomogeneous symmetry breaking induced by an inhomogeneous gravitational field.
Excitations in photoactive molecules from quantum Monte Carlo
International Nuclear Information System (INIS)
Despite significant advances in electronic structure methods for the treatment of excited states, attaining an accurate description of the photoinduced processes in photoactive biomolecules is proving very difficult. For the prototypical photosensitive molecules, formaldimine, formaldehyde, and a minimal protonated Schiff base model of the retinal chromophore, we investigate the performance of various approaches generally considered promising for the computation of excited potential energy surfaces. We show that quantum Monte Carlo can accurately estimate the excitation energies of the studied systems if one constructs carefully the trial wave function, including in most cases the reoptimization of its determinantal part within quantum Monte Carlo. While time-dependent density functional theory and quantum Monte Carlo are generally in reasonable agreement, they yield a qualitatively different description of the isomerization of the Schiff base model. Finally, we find that the restricted open shell Kohn-Sham method is at variance with quantum Monte Carlo in estimating the lowest-singlet excited state potential energy surface for low-symmetry molecular structures
Monte-carlo calculations for some problems of quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Novoselov, A. A., E-mail: novoselov@goa.bog.msu.ru; Pavlovsky, O. V.; Ulybyshev, M. V. [Moscow State University (Russian Federation)
2012-09-15
The Monte-Carlo technique for the calculations of functional integral in two one-dimensional quantum-mechanical problems had been applied. The energies of the bound states in some potential wells were obtained using this method. Also some peculiarities in the calculation of the kinetic energy in the ground state had been studied.
Monte-carlo calculations for some problems of quantum mechanics
International Nuclear Information System (INIS)
The Monte-Carlo technique for the calculations of functional integral in two one-dimensional quantum-mechanical problems had been applied. The energies of the bound states in some potential wells were obtained using this method. Also some peculiarities in the calculation of the kinetic energy in the ground state had been studied.
Quantum Monte Carlo calculations of light nuclei using chiral potentials
Lynn, J E; Epelbaum, E; Gandolfi, S; Gezerlis, A; Schwenk, A
2014-01-01
We present the first Green's function Monte Carlo calculations of light nuclei with nuclear interactions derived from chiral effective field theory up to next-to-next-to-leading order. Up to this order, the interactions can be constructed in local form and are therefore amenable to quantum Monte Carlo calculations. We demonstrate a systematic improvement with each order for the binding energies of $A=3$ and $A=4$ systems. We also carry out the first few-body tests to study perturbative expansions of chiral potentials at different orders, finding that higher-order corrections are more perturbative for softer interactions. Our results confirm the necessity of a three-body force for correct reproduction of experimental binding energies and radii, and pave the way for studying few- and many-nucleon systems using quantum Monte Carlo methods with chiral interactions.
Properties of Reactive Oxygen Species by Quantum Monte Carlo
Zen, Andrea; Guidoni, Leonardo
2014-01-01
The electronic properties of the oxygen molecule, in its singlet and triplet states, and of many small oxygen-containing radicals and anions have important roles in different fields of Chemistry, Biology and Atmospheric Science. Nevertheless, the electronic structure of such species is a challenge for ab-initio computational approaches because of the difficulties to correctly describe the statical and dynamical correlation effects in presence of one or more unpaired electrons. Only the highest-level quantum chemical approaches can yield reliable characterizations of their molecular properties, such as binding energies, equilibrium structures, molecular vibrations, charge distribution and polarizabilities. In this work we use the variational Monte Carlo (VMC) and the lattice regularized Monte Carlo (LRDMC) methods to investigate the equilibrium geometries and molecular properties of oxygen and oxygen reactive species. Quantum Monte Carlo methods are used in combination with the Jastrow Antisymmetrized Geminal ...
Multi-Determinant Wave-functions in Quantum Monte Carlo
Energy Technology Data Exchange (ETDEWEB)
Morales, Miguel A [Lawrence Livermore National Laboratory (LLNL); Mcminis, Jeremy [University of Illinois, Urbana-Champaign; Clark, Bryan K. [Princeton University; Kim, Jeongnim [ORNL; Scuseria, Gustavo E [Rice University
2012-01-01
Quantum Monte Carlo methods have received considerable attention over the last decades due to the great promise they have for the direct solution to the many-body Schrodinger equation for electronic systems. Thanks to a low scaling with number of particles, they present one of the best alternatives in the accurate study of large systems and solid state calculations. In spite of such promise, the method has not become popular in the quantum chemistry community, mainly due to the lack of control over the fixed-node error which can be large in many cases. In this article we present the application of large multi-determinant expansions in quantum Monte Carlo, studying its performance with first row dimers and the 55 molecules of the G1 test set. We demonstrate the potential of the wave-function to systematically reduce the fixed-node error in the calculations, achieving chemical accuracy in almost all cases studied. When compared to traditional methods in quantum chemistry, the results show a marked improvement over most methods including MP2, CCSD(T) and DFT with various functionals; in fact the only method able to produce better results is the explicitly-correlated CCSD(T) method with a large basis set. With recent developments in trial wave functions and algorithmic improvements in Quantum Monte Carlo, we are quickly approaching a time where the method can become the standard in the study of large molecular systems and solids.
Variation After Response in Quantum Monte Carlo
Neuscamman, Eric
2016-01-01
We present a new method for modeling electronically excited states that overcomes a key failing of linear response theory by allowing the underlying ground state ansatz to relax in the presence of an excitation. The method is variational, has a cost similar to ground state variational Monte Carlo, and admits both open and periodic boundary conditions. We present preliminary numerical results showing that, when paired with the Jastrow antisymmetric geminal power ansatz, the variation-after-response formalism delivers accuracies for valence and charge transfer single excitations on par with equation of motion coupled cluster, while surpassing even this very high-level method's accuracy for excitations with significant doubly excited character.
Chemical accuracy from quantum Monte Carlo for the benzene dimer.
Azadi, Sam; Cohen, R E
2015-09-14
We report an accurate study of interactions between benzene molecules using variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods. We compare these results with density functional theory using different van der Waals functionals. In our quantum Monte Carlo (QMC) calculations, we use accurate correlated trial wave functions including three-body Jastrow factors and backflow transformations. We consider two benzene molecules in the parallel displaced geometry, and find that by highly optimizing the wave function and introducing more dynamical correlation into the wave function, we compute the weak chemical binding energy between aromatic rings accurately. We find optimal VMC and DMC binding energies of -2.3(4) and -2.7(3) kcal/mol, respectively. The best estimate of the coupled-cluster theory through perturbative triplets/complete basis set limit is -2.65(2) kcal/mol [Miliordos et al., J. Phys. Chem. A 118, 7568 (2014)]. Our results indicate that QMC methods give chemical accuracy for weakly bound van der Waals molecular interactions, comparable to results from the best quantum chemistry methods. PMID:26374029
Chemical accuracy from quantum Monte Carlo for the benzene dimer
International Nuclear Information System (INIS)
We report an accurate study of interactions between benzene molecules using variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods. We compare these results with density functional theory using different van der Waals functionals. In our quantum Monte Carlo (QMC) calculations, we use accurate correlated trial wave functions including three-body Jastrow factors and backflow transformations. We consider two benzene molecules in the parallel displaced geometry, and find that by highly optimizing the wave function and introducing more dynamical correlation into the wave function, we compute the weak chemical binding energy between aromatic rings accurately. We find optimal VMC and DMC binding energies of −2.3(4) and −2.7(3) kcal/mol, respectively. The best estimate of the coupled-cluster theory through perturbative triplets/complete basis set limit is −2.65(2) kcal/mol [Miliordos et al., J. Phys. Chem. A 118, 7568 (2014)]. Our results indicate that QMC methods give chemical accuracy for weakly bound van der Waals molecular interactions, comparable to results from the best quantum chemistry methods
Strategies for improving the efficiency of quantum Monte Carlo calculations
Lee, R M; Nemec, N; Rios, P Lopez; Drummond, N D
2010-01-01
We describe a number of strategies for optimizing the efficiency of quantum Monte Carlo (QMC) calculations. We investigate the dependence of the efficiency of the variational Monte Carlo method on the sampling algorithm. Within a unified framework, we compare several commonly used variants of diffusion Monte Carlo (DMC). We then investigate the behavior of DMC calculations on parallel computers and the details of parallel implementations, before proposing a technique to optimize the efficiency of the extrapolation of DMC results to zero time step, finding that a relative time step ratio of 1:4 is optimal. Finally, we discuss the removal of serial correlation from data sets by reblocking, setting out criteria for the choice of block length and quantifying the effects of the uncertainty in the estimated correlation length and the presence of divergences in the local energy on estimated error bars on QMC energies.
Infinite variance in fermion quantum Monte Carlo calculations
Shi, Hao; Zhang, Shiwei
2016-03-01
For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties without the sign problem. The list spans condensed matter, nuclear physics, and high-energy physics, including the half-filled repulsive Hubbard model, the spin-balanced atomic Fermi gas, and lattice quantum chromodynamics calculations at zero density with Wilson Fermions, and is growing rapidly as a number of problems have been discovered recently to be free of the sign problem. In these situations, QMC calculations are relied on to provide definitive answers. Their results are instrumental to our ability to understand and compute properties in fundamental models important to multiple subareas in quantum physics. It is shown, however, that the most commonly employed algorithms in such situations have an infinite variance problem. A diverging variance causes the estimated Monte Carlo statistical error bar to be incorrect, which can render the results of the calculation unreliable or meaningless. We discuss how to identify the infinite variance problem. An approach is then proposed to solve the problem. The solution does not require major modifications to standard algorithms, adding a "bridge link" to the imaginary-time path integral. The general idea is applicable to a variety of situations where the infinite variance problem may be present. Illustrative results are presented for the ground state of the Hubbard model at half-filling.
Quantum Monte Carlo study of the protonated water dimer
Dagrada, Mario; Saitta, Antonino M; Sorella, Sandro; Mauri, Francesco
2013-01-01
We report an extensive theoretical study of the protonated water dimer (Zundel ion) by means of the highly correlated variational Monte Carlo and lattice regularized Monte Carlo approaches. This system represents the simplest model for proton transfer (PT) and a correct description of its properties is essential in order to understand the PT mechanism in more complex acqueous systems. Our Jastrow correlated AGP wave function ensures an accurate treatment of electron correlations. Exploiting the advantages of contracting the primitive basis set over atomic hybrid orbitals, we are able to limit dramatically the number of variational parameters with a systematic control on the numerical precision, crucial in order to simulate larger systems. We investigate energetics and geometrical properties of the Zundel ion as a function of the oxygen-oxygen distance, taken as reaction coordinate. In both cases, our QMC results are found in excellent agreement with coupled cluster CCSD(T) technique, the quantum chemistry "go...
Binnie, S. J.; Nolan, S. J.; Drummond, Neil; Alfe`, D.; Allan, N. L; Manby, F. R.; Gillan, M. J.
2010-01-01
We show how accurate benchmark values of the surface formation energy of crystalline lithium hydride can be computed by the complementary techniques of quantum Monte Carlo (QMC) and wavefunction-based molecular quantum chemistry. To demonstrate the high accuracy of the QMC techniques, we present a detailed study of the energetics of the bulk LiH crystal, using both pseudopotential and all-electron approaches. We show that the equilibrium lattice parameter agrees with experiment to within 0.03...
The energetics of oxide surfaces by quantum Monte Carlo
International Nuclear Information System (INIS)
Density functional theory (DFT) is widely used in surface science, but for some properties the predictions depend strongly on the approximation used for exchange-correlation energy. We note recent suggestions that the widely used generalized gradient approximation (GGA) is inferior to the local density approximation (LDA) for the surface formation energy σ of both transition metals and oxides. We report quantum Monte Carlo calculations of σ for the MgO(001) surface which support the accuracy of LDA for this case, and indicate that GGA is too low by ∼30%. We point out the potentially important implications of this result for nanoscience modelling. (letter to the editor)
Spinor path integral Quantum Monte Carlo for fermions
Shin, Daejin; Yousif, Hosam; Shumway, John
2007-03-01
We have developed a continuous-space path integral method for spin 1/2 fermions with fixed-phase approximation. The internal spin degrees of freedom of each particle is represented by four extra dimensions. This effectively maps each spinor onto two of the excited states of a four dimensional harmonic oscillator. The phases that appear in the problem can be treated within the fixed-phase approximation. This mapping preserves rotational invariance and allows us to treat spin interactions and fermionic exchange on equal footing, which may lead to new theoretical insights. The technique is illustrated for a few simple models, including a spin in a magnetic field and interacting electrons in a quantum dot in a magnetic field at finite temperature. We will discuss possible extensions of the method to molecules and solids using variational and diffusion Quantum Monte Carlo.
Chemical accuracy from quantum Monte Carlo for the Benzene Dimer
Azadi, Sam
2015-01-01
We report an accurate study of interactions between Benzene molecules using variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods. We compare these results with density functional theory (DFT) using different van der Waals (vdW) functionals. In our QMC calculations, we use accurate correlated trial wave functions including three-body Jastrow factors, and backflow transformations. We consider two benzene molecules in the parallel displaced (PD) geometry, and find that by highly optimizing the wave function and introducing more dynamical correlation into the wave function, we compute the weak chemical binding energy between aromatic rings accurately. We find optimal VMC and DMC binding energies of -2.3(4) and -2.7(3) kcal/mol, respectively. The best estimate of the CCSD(T)/CBS limit is -2.65(2) kcal/mol [E. Miliordos et al, J. Phys. Chem. A 118, 7568 (2014)]. Our results indicate that QMC methods give chemical accuracy for weakly bound van der Waals molecular interactions, compar...
Infinite Variance in Fermion Quantum Monte Carlo Calculations
Shi, Hao
2015-01-01
For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties, without the sign problem. The list spans condensed matter, nuclear physics, and high-energy physics, including the half-filled repulsive Hubbard model, the spin-balanced atomic Fermi gas, lattice QCD calculations at zero density with Wilson Fermions, and is growing rapidly as a number of problems have been discovered recently to be free of the sign problem. In these situations, QMC calculations are relied upon to provide definitive answers. Their results are instrumental to our ability to understand and compute properties in fundamental models important to multiple sub-areas in quantum physics. It is shown, however, that the most commonly employed algorithms in such situations turn out to have an infinite variance problem. A diverging variance causes the estimated Monte Carlo statistical error bar to be incorrect, which can render the results of the calc...
Properties of reactive oxygen species by quantum Monte Carlo
Energy Technology Data Exchange (ETDEWEB)
Zen, Andrea [Dipartimento di Fisica, La Sapienza - Università di Roma, Piazzale Aldo Moro 2, 00185 Rome (Italy); Trout, Bernhardt L. [Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, Massachusetts 02139 (United States); Guidoni, Leonardo, E-mail: leonardo.guidoni@univaq.it [Dipartimento di Scienze Fisiche e Chimiche, Università degli studi de L' Aquila, Via Vetoio, 67100 Coppito, L' Aquila (Italy)
2014-07-07
The electronic properties of the oxygen molecule, in its singlet and triplet states, and of many small oxygen-containing radicals and anions have important roles in different fields of chemistry, biology, and atmospheric science. Nevertheless, the electronic structure of such species is a challenge for ab initio computational approaches because of the difficulties to correctly describe the statical and dynamical correlation effects in presence of one or more unpaired electrons. Only the highest-level quantum chemical approaches can yield reliable characterizations of their molecular properties, such as binding energies, equilibrium structures, molecular vibrations, charge distribution, and polarizabilities. In this work we use the variational Monte Carlo (VMC) and the lattice regularized Monte Carlo (LRDMC) methods to investigate the equilibrium geometries and molecular properties of oxygen and oxygen reactive species. Quantum Monte Carlo methods are used in combination with the Jastrow Antisymmetrized Geminal Power (JAGP) wave function ansatz, which has been recently shown to effectively describe the statical and dynamical correlation of different molecular systems. In particular, we have studied the oxygen molecule, the superoxide anion, the nitric oxide radical and anion, the hydroxyl and hydroperoxyl radicals and their corresponding anions, and the hydrotrioxyl radical. Overall, the methodology was able to correctly describe the geometrical and electronic properties of these systems, through compact but fully-optimised basis sets and with a computational cost which scales as N{sup 3} − N{sup 4}, where N is the number of electrons. This work is therefore opening the way to the accurate study of the energetics and of the reactivity of large and complex oxygen species by first principles.
Aoki, Shuntaro
2016-01-01
We reconsider the relation between three supergravity formalisms with different sets of auxiliary fields, known as the old-, new-, and non-minimal supergravity. Although it has been known that the old minimal formulation is the broadest class, we find that, with an unphysical $U(1)$ gauge symmetry and a compensating superfield, all of them become completely equivalent.
Quantum Monte Carlo study of bilayer ionic Hubbard model
Jiang, M.; Schulthess, T. C.
2016-04-01
The interaction-driven insulator-to-metal transition has been reported in the ionic Hubbard model (IHM) for moderate interaction U , while its metallic phase only occupies a narrow region in the phase diagram. To explore the enlargement of the metallic regime, we extend the ionic Hubbard model to two coupled layers and study the interplay of interlayer hybridization V and two types of intralayer staggered potentials Δ : one with the same (in-phase) and the other with a π -phase shift (antiphase) potential between layers. Our determinant quantum Monte Carlo (DQMC) simulations at lowest accessible temperatures demonstrate that the interaction-driven metallic phase between Mott and band insulators expands in the Δ -V phase diagram of bilayer IHM only for in-phase ionic potentials; while antiphase potential always induces an insulator with charge density order. This implies possible further extension of the ionic Hubbard model from the bilayer case here to a realistic three-dimensional model.
Continuous-time quantum Monte Carlo using worm sampling
Gunacker, P.; Wallerberger, M.; Gull, E.; Hausoel, A.; Sangiovanni, G.; Held, K.
2015-10-01
We present a worm sampling method for calculating one- and two-particle Green's functions using continuous-time quantum Monte Carlo simulations in the hybridization expansion (CT-HYB). Instead of measuring Green's functions by removing hybridization lines from partition function configurations, as in conventional CT-HYB, the worm algorithm directly samples the Green's function. We show that worm sampling is necessary to obtain general two-particle Green's functions which are not of density-density type and that it improves the sampling efficiency when approaching the atomic limit. Such two-particle Green's functions are needed to compute off-diagonal elements of susceptibilities and occur in diagrammatic extensions of the dynamical mean-field theory and in efficient estimators for the single-particle self-energy.
Quantum states of confined hydrogen plasma species: Monte Carlo calculations
Micca Longo, G.; Longo, S.; Giordano, D.
2015-12-01
The diffusion Monte Carlo method with symmetry-based state selection is used to calculate the quantum energy states of \\text{H}2+ confined into potential barriers of atomic dimensions (a model for these ions in solids). Special solutions are employed, permitting one to obtain satisfactory results with rather simple native code. As a test case, {{}2}{{\\Pi}u} and {{}2}{{\\Pi}g} states of \\text{H}2+ ions under spherical confinement are considered. The results are interpreted using the correlation of \\text{H}2+ states to atomic orbitals of H atoms lying on the confining surface and perturbation calculations. The method is straightforwardly applied to cavities of any shape and different hydrogen plasma species (at least one-electron ones, including H) for future studies with real crystal symmetries.
Monte Carlo simulations of quantum systems on massively parallel supercomputers
International Nuclear Information System (INIS)
A large class of quantum physics applications uses operator representations that are discrete integers by nature. This class includes magnetic properties of solids, interacting bosons modeling superfluids and Cooper pairs in superconductors, and Hubbard models for strongly correlated electrons systems. This kind of application typically uses integer data representations and the resulting algorithms are dominated entirely by integer operations. The authors implemented an efficient algorithm for one such application on the Intel Touchstone Delta and iPSC/860. The algorithm uses a multispin coding technique which allows significant data compactification and efficient vectorization of Monte Carlo updates. The algorithm regularly switches between two data decompositions, corresponding naturally to different Monte Carlo updating processes and observable measurements such that only nearest-neighbor communications are needed within a given decomposition. On 128 nodes of Intel Delta, this algorithm updates 183 million spins per second (compared to 21 million on CM-2 and 6.2 million on a Cray Y-MP). A systematic performance analysis shows a better than 90% efficiency in the parallel implementation
Two- and Three-Nucleon Chiral Interactions in Quantum Monte Carlo Calculations for Nuclear Physics
Lynn, Joel; Carlson, Joseph; Gandolfi, Stefano; Gezerlis, Alexandros; Schmidt, Kevin; Schwenk, Achim; Tews, Ingo
2015-10-01
I present our recent work on Green's function Monte Carlo (GFMC) calculations of light nuclei using local two- and three-nucleon interactions derived from chiral effective field theory (EFT) up to next-to-next-to-leading order (N2LO). GFMC provides important benchmarking capabilities for other methods which rely on techniques to soften the nuclear interaction and also allows for nonperturbative studies of the convergence of the chiral EFT expansion. I discuss the choice of observables we make to fit the two low-energy constants which enter in the three-nucleon sector at N2LO: the 4He binding energy and n- α elastic scattering P-wave phase shifts. I then show some results for light nuclei. I also show our results for the energy per neutron in pure neutron matter using the auxiliary-field diffusion Monte Carlo method and discuss regulator choices. Finally I discuss some exciting future projects which are now possible. The NUCLEI SciDAC program and the National Energy Research Scientific Computing Center (NERSC), which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.
Quantum Monte Carlo with very large multideterminant wavefunctions.
Scemama, Anthony; Applencourt, Thomas; Giner, Emmanuel; Caffarel, Michel
2016-07-01
An algorithm to compute efficiently the first two derivatives of (very) large multideterminant wavefunctions for quantum Monte Carlo calculations is presented. The calculation of determinants and their derivatives is performed using the Sherman-Morrison formula for updating the inverse Slater matrix. An improved implementation based on the reduction of the number of column substitutions and on a very efficient implementation of the calculation of the scalar products involved is presented. It is emphasized that multideterminant expansions contain in general a large number of identical spin-specific determinants: for typical configuration interaction-type wavefunctions the number of unique spin-specific determinants Ndetσ ( σ=↑,↓) with a non-negligible weight in the expansion is of order O(Ndet). We show that a careful implementation of the calculation of the Ndet -dependent contributions can make this step negligible enough so that in practice the algorithm scales as the total number of unique spin-specific determinants, Ndet↑+Ndet↓, over a wide range of total number of determinants (here, Ndet up to about one million), thus greatly reducing the total computational cost. Finally, a new truncation scheme for the multideterminant expansion is proposed so that larger expansions can be considered without increasing the computational time. The algorithm is illustrated with all-electron fixed-node diffusion Monte Carlo calculations of the total energy of the chlorine atom. Calculations using a trial wavefunction including about 750,000 determinants with a computational increase of ∼400 compared to a single-determinant calculation are shown to be feasible. © 2016 Wiley Periodicals, Inc. PMID:27302337
Quantum Monte Carlo Algorithms for Diagrammatic Vibrational Structure Calculations
Hermes, Matthew; Hirata, So
2015-06-01
Convergent hierarchies of theories for calculating many-body vibrational ground and excited-state wave functions, such as Møller-Plesset perturbation theory or coupled cluster theory, tend to rely on matrix-algebraic manipulations of large, high-dimensional arrays of anharmonic force constants, tasks which require large amounts of computer storage space and which are very difficult to implement in a parallel-scalable fashion. On the other hand, existing quantum Monte Carlo (QMC) methods for vibrational wave functions tend to lack robust techniques for obtaining excited-state energies, especially for large systems. By exploiting analytical identities for matrix elements of position operators in a harmonic oscillator basis, we have developed stochastic implementations of the size-extensive vibrational self-consistent field (MC-XVSCF) and size-extensive vibrational Møller-Plesset second-order perturbation (MC-XVMP2) theories which do not require storing the potential energy surface (PES). The programmable equations of MC-XVSCF and MC-XVMP2 take the form of a small number of high-dimensional integrals evaluated using Metropolis Monte Carlo techniques. The associated integrands require independent evaluations of only the value, not the derivatives, of the PES at many points, a task which is trivial to parallelize. However, unlike existing vibrational QMC methods, MC-XVSCF and MC-XVMP2 can calculate anharmonic frequencies directly, rather than as a small difference between two noisy total energies, and do not require user-selected coordinates or nodal surfaces. MC-XVSCF and MC-XVMP2 can also directly sample the PES in a given approximation without analytical or grid-based approximations, enabling us to quantify the errors induced by such approximations.
Quantum Monte Carlo for electronic structure: Recent developments and applications
International Nuclear Information System (INIS)
Quantum Monte Carlo (QMC) methods have been found to give excellent results when applied to chemical systems. The main goal of the present work is to use QMC to perform electronic structure calculations. In QMC, a Monte Carlo simulation is used to solve the Schroedinger equation, taking advantage of its analogy to a classical diffusion process with branching. In the present work the author focuses on how to extend the usefulness of QMC to more meaningful molecular systems. This study is aimed at questions concerning polyatomic and large atomic number systems. The accuracy of the solution obtained is determined by the accuracy of the trial wave function's nodal structure. Efforts in the group have given great emphasis to finding optimized wave functions for the QMC calculations. Little work had been done by systematically looking at a family of systems to see how the best wave functions evolve with system size. In this work the author presents a study of trial wave functions for C, CH, C2H and C2H2. The goal is to study how to build wave functions for larger systems by accumulating knowledge from the wave functions of its fragments as well as gaining some knowledge on the usefulness of multi-reference wave functions. In a MC calculation of a heavy atom, for reasonable time steps most moves for core electrons are rejected. For this reason true equilibration is rarely achieved. A method proposed by Batrouni and Reynolds modifies the way the simulation is performed without altering the final steady-state solution. It introduces an acceleration matrix chosen so that all coordinates (i.e., of core and valence electrons) propagate at comparable speeds. A study of the results obtained using their proposed matrix suggests that it may not be the optimum choice. In this work the author has found that the desired mixing of coordinates between core and valence electrons is not achieved when using this matrix. A bibliography of 175 references is included
Quantum Monte Carlo Calculations Applied to Magnetic Molecules
International Nuclear Information System (INIS)
We have calculated the equilibrium thermodynamic properties of Heisenberg spin systems using a quantum Monte Carlo (QMC) method. We have used some of these systems as models to describe recently synthesized magnetic molecules, and-upon comparing the results of these calculations with experimental data-have obtained accurate estimates for the basic parameters of these models. We have also performed calculations for other systems that are of more general interest, being relevant both for existing experimental data and for future experiments. Utilizing the concept of importance sampling, these calculations can be carried out in an arbitrarily large quantum Hilbert space, while still avoiding any approximations that would introduce systematic errors. The only errors are statistical in nature, and as such, their magnitudes are accurately estimated during the course of a simulation. Frustrated spin systems present a major challenge to the QMC method, nevertheless, in many instances progress can be made. In this chapter, the field of magnetic molecules is introduced, paying particular attention to the characteristics that distinguish magnetic molecules from other systems that are studied in condensed matter physics. We briefly outline the typical path by which we learn about magnetic molecules, which requires a close relationship between experiments and theoretical calculations. The typical experiments are introduced here, while the theoretical methods are discussed in the next chapter. Each of these theoretical methods has a considerable limitation, also described in Chapter 2, which together serve to motivate the present work. As is shown throughout the later chapters, the present QMC method is often able to provide useful information where other methods fail. In Chapter 3, the use of Monte Carlo methods in statistical physics is reviewed, building up the fundamental ideas that are necessary in order to understand the method that has been used in this work. With these
Quantum Monte Carlo Calculations Applied to Magnetic Molecules
Energy Technology Data Exchange (ETDEWEB)
Larry Engelhardt
2006-08-09
We have calculated the equilibrium thermodynamic properties of Heisenberg spin systems using a quantum Monte Carlo (QMC) method. We have used some of these systems as models to describe recently synthesized magnetic molecules, and-upon comparing the results of these calculations with experimental data-have obtained accurate estimates for the basic parameters of these models. We have also performed calculations for other systems that are of more general interest, being relevant both for existing experimental data and for future experiments. Utilizing the concept of importance sampling, these calculations can be carried out in an arbitrarily large quantum Hilbert space, while still avoiding any approximations that would introduce systematic errors. The only errors are statistical in nature, and as such, their magnitudes are accurately estimated during the course of a simulation. Frustrated spin systems present a major challenge to the QMC method, nevertheless, in many instances progress can be made. In this chapter, the field of magnetic molecules is introduced, paying particular attention to the characteristics that distinguish magnetic molecules from other systems that are studied in condensed matter physics. We briefly outline the typical path by which we learn about magnetic molecules, which requires a close relationship between experiments and theoretical calculations. The typical experiments are introduced here, while the theoretical methods are discussed in the next chapter. Each of these theoretical methods has a considerable limitation, also described in Chapter 2, which together serve to motivate the present work. As is shown throughout the later chapters, the present QMC method is often able to provide useful information where other methods fail. In Chapter 3, the use of Monte Carlo methods in statistical physics is reviewed, building up the fundamental ideas that are necessary in order to understand the method that has been used in this work. With these
Calkins, Mathew; Gates, D.(Center for String and Particle Theory, Department of Physics, University of Maryland, College Park, MD, 20742-4111, U.S.A.); Gates, S.(Center for String and Particle Theory, Department of Physics, University of Maryland, College Park, MD, 20742-4111, U.S.A.); Golding, William(Sensors and Electron Devices Directorate, US Army Research Laboratory, Adelphi, Maryland, 20783, U.S.A.)
2015-01-01
Starting with valise supermultiplets obtained from 0-branes plus field redefinitions, valise adinkra networks, and the "Garden Algebra," we discuss an architecture for algorithms that (starting from on-shell theories and, through a well-defined computation procedure), search for off-shell completions. We show in one dimension how to directly attack the notorious "off-shell auxiliary field" problem of supersymmetry with algorithms in the adinkra network-world formulation.
Calkins, Mathew; Gates,, S James; Golding, William M
2015-01-01
Starting with valise supermultiplets obtained from 0-branes plus field redefinitions, valise adinkra networks, and the "Garden Algebra," we discuss an architecture for algorithms that (starting from on-shell theories and, through a well-defined computation procedure), search for off-shell completions. We show in one dimension how to directly attack the notorious "off-shell auxiliary field" problem of supersymmetry with algorithms in the adinkra network-world formulation.
Calkins, Mathew; Gates, D. E. A.; Gates, S. James; Golding, William M.
2015-04-01
Starting with valise supermultiplets obtained from 0-branes plus field redefinitions, valise adinkra networks, and the "Garden Algebra," we discuss an architecture for algorithms that (starting from on-shell theories and, through a well-defined computation procedure), search for off-shell completions. We show in one dimension how to directly attack the notorious "off-shell auxiliary field" problem of supersymmetry with algorithms in the adinkra network-world formulation.
Energy Technology Data Exchange (ETDEWEB)
Burkatzki, Mark Thomas
2008-07-01
The author presents scalar-relativistic energy-consistent Hartree-Fock pseudopotentials for the main-group and 3d-transition-metal elements. The pseudopotentials do not exhibit a singularity at the nucleus and are therefore suitable for quantum Monte Carlo (QMC) calculations. The author demonstrates their transferability through extensive benchmark calculations of atomic excitation spectra as well as molecular properties. In particular, the author computes the vibrational frequencies and binding energies of 26 first- and second-row diatomic molecules using post Hartree-Fock methods, finding excellent agreement with the corresponding all-electron values. The author shows that the presented pseudopotentials give superior accuracy than other existing pseudopotentials constructed specifically for QMC. The localization error and the efficiency in QMC are discussed. The author also presents QMC calculations for selected atomic and diatomic 3d-transitionmetal systems. Finally, valence basis sets of different sizes (VnZ with n=D,T,Q,5 for 1st and 2nd row; with n=D,T for 3rd to 5th row; with n=D,T,Q for the 3d transition metals) optimized for the pseudopotentials are presented. (orig.)
Cohesion energetics of carbon allotropes: Quantum Monte Carlo study
International Nuclear Information System (INIS)
We have performed quantum Monte Carlo calculations to study the cohesion energetics of carbon allotropes, including sp3-bonded diamond, sp2-bonded graphene, sp–sp2 hybridized graphynes, and sp-bonded carbyne. The computed cohesive energies of diamond and graphene are found to be in excellent agreement with the corresponding values determined experimentally for diamond and graphite, respectively, when the zero-point energies, along with the interlayer binding in the case of graphite, are included. We have also found that the cohesive energy of graphyne decreases systematically as the ratio of sp-bonded carbon atoms increases. The cohesive energy of γ-graphyne, the most energetically stable graphyne, turns out to be 6.766(6) eV/atom, which is smaller than that of graphene by 0.698(12) eV/atom. Experimental difficulty in synthesizing graphynes could be explained by their significantly smaller cohesive energies. Finally, we conclude that the cohesive energy of a newly proposed graphyne can be accurately estimated with the carbon–carbon bond energies determined from the cohesive energies of graphene and three different graphynes considered here
A Novel Exact Fixed-node Quantum Monte Carlo Algorithm
Institute of Scientific and Technical Information of China (English)
Hong Xin HUANG
2004-01-01
In this paper we proposed a novel exact fixed-node quantum Monte Carlo (EFNQMC) algorithm, which is a self-optimizing and self-improving procedure. In contrast to the previous EFNQMC method, the trial function is optimized synchronistically in the diffusion procedure, but not before the beginning of EFNQMC computation. In order to optimize the trial function, the improved steepest descent technique is used, in which the step size is automatically adjustable. The procedure is quasi-Newton and converges super linearly. We also use a novel trial function, which has correct electron-electron and electron-nucleus cusp conditions. The novel EFNQMC algorithm and the novel trial function are employed to calculate the energies of 11A1 state of CH2, 1Ag state of C8 and the ground-states of H2, LiH, Li2, H2O, respectively. The test results show that both the novel algorithm and the trial function proposed in the present paper are very excellent.
Magnetism of iron and nickel from rotationally invariant Hirsch-Fye quantum Monte Carlo calculations
Belozerov, A. S.; Leonov, I.; Anisimov, V. I.
2013-01-01
We present a rotationally invariant Hirsch-Fye quantum Monte Carlo algorithm in which the spin rotational invariance of Hund's exchange is approximated by averaging over all possible directions of the spin quantization axis. We employ this technique to perform benchmark calculations for the two- and three-band Hubbard models on the infinite-dimensional Bethe lattice. Our results agree quantitatively well with those obtained using the continuous-time quantum Monte Carlo method with rotationall...
Quantum dynamics at finite temperature: Time-dependent quantum Monte Carlo study
Christov, Ivan P.
2016-08-01
In this work we investigate the ground state and the dissipative quantum dynamics of interacting charged particles in an external potential at finite temperature. The recently devised time-dependent quantum Monte Carlo (TDQMC) method allows a self-consistent treatment of the system of particles together with bath oscillators first for imaginary-time propagation of Schrödinger type of equations where both the system and the bath converge to their finite temperature ground state, and next for real time calculation where the dissipative dynamics is demonstrated. In that context the application of TDQMC appears as promising alternative to the path-integral related techniques where the real time propagation can be a challenge.
Quantum Monte Carlo for electronic structure: Recent developments and applications
Energy Technology Data Exchange (ETDEWEB)
Rodriquez, M. M.S. [Lawrence Berkeley Lab. and Univ. of California, Berkeley, CA (United States). Dept. of Chemistry
1995-04-01
Quantum Monte Carlo (QMC) methods have been found to give excellent results when applied to chemical systems. The main goal of the present work is to use QMC to perform electronic structure calculations. In QMC, a Monte Carlo simulation is used to solve the Schroedinger equation, taking advantage of its analogy to a classical diffusion process with branching. In the present work the author focuses on how to extend the usefulness of QMC to more meaningful molecular systems. This study is aimed at questions concerning polyatomic and large atomic number systems. The accuracy of the solution obtained is determined by the accuracy of the trial wave function`s nodal structure. Efforts in the group have given great emphasis to finding optimized wave functions for the QMC calculations. Little work had been done by systematically looking at a family of systems to see how the best wave functions evolve with system size. In this work the author presents a study of trial wave functions for C, CH, C{sub 2}H and C{sub 2}H{sub 2}. The goal is to study how to build wave functions for larger systems by accumulating knowledge from the wave functions of its fragments as well as gaining some knowledge on the usefulness of multi-reference wave functions. In a MC calculation of a heavy atom, for reasonable time steps most moves for core electrons are rejected. For this reason true equilibration is rarely achieved. A method proposed by Batrouni and Reynolds modifies the way the simulation is performed without altering the final steady-state solution. It introduces an acceleration matrix chosen so that all coordinates (i.e., of core and valence electrons) propagate at comparable speeds. A study of the results obtained using their proposed matrix suggests that it may not be the optimum choice. In this work the author has found that the desired mixing of coordinates between core and valence electrons is not achieved when using this matrix. A bibliography of 175 references is included.
Das, Arnab; Chakrabarti, Bikas K.
2008-12-01
Here we discuss the annealing behavior of an infinite-range ±J Ising spin glass in the presence of a transverse field using a zero-temperature quantum Monte Carlo method. Within the simulation scheme, we demonstrate that quantum annealing not only helps finding the ground state of a classical spin glass, but can also help simulating the ground state of a quantum spin glass, in particular, when the transverse field is low, much more efficiently.
Approaching the Ground State of a Quantum Spin Glass using a Zero-Temperature Quantum Monte Carlo
Das, Arnab; Chakrabarti, Bikas K.
2008-01-01
Here we discuss the annealing behavior of an infinite-range $\\pm J$ Ising spin glass in presence of a transverse field using a zero-temperature quantum Monte Carlo. Within the simulation scheme, we demonstrate that quantum annealing not only helps finding the ground state of a classical spin glass, but can also help simulating the ground state of a quantum spin glass, in particularly, when the transverse field is low, much more efficiently.
Quantum Monte Carlo methods and lithium cluster properties. [Atomic clusters
Energy Technology Data Exchange (ETDEWEB)
Owen, R.K.
1990-12-01
Properties of small lithium clusters with sizes ranging from n = 1 to 5 atoms were investigated using quantum Monte Carlo (QMC) methods. Cluster geometries were found from complete active space self consistent field (CASSCF) calculations. A detailed development of the QMC method leading to the variational QMC (V-QMC) and diffusion QMC (D-QMC) methods is shown. The many-body aspect of electron correlation is introduced into the QMC importance sampling electron-electron correlation functions by using density dependent parameters, and are shown to increase the amount of correlation energy obtained in V-QMC calculations. A detailed analysis of D-QMC time-step bias is made and is found to be at least linear with respect to the time-step. The D-QMC calculations determined the lithium cluster ionization potentials to be 0.1982(14) (0.1981), 0.1895(9) (0.1874(4)), 0.1530(34) (0.1599(73)), 0.1664(37) (0.1724(110)), 0.1613(43) (0.1675(110)) Hartrees for lithium clusters n = 1 through 5, respectively; in good agreement with experimental results shown in the brackets. Also, the binding energies per atom was computed to be 0.0177(8) (0.0203(12)), 0.0188(10) (0.0220(21)), 0.0247(8) (0.0310(12)), 0.0253(8) (0.0351(8)) Hartrees for lithium clusters n = 2 through 5, respectively. The lithium cluster one-electron density is shown to have charge concentrations corresponding to nonnuclear attractors. The overall shape of the electronic charge density also bears a remarkable similarity with the anisotropic harmonic oscillator model shape for the given number of valence electrons.
Quantum Monte Carlo methods and lithium cluster properties
Energy Technology Data Exchange (ETDEWEB)
Owen, R.K.
1990-12-01
Properties of small lithium clusters with sizes ranging from n = 1 to 5 atoms were investigated using quantum Monte Carlo (QMC) methods. Cluster geometries were found from complete active space self consistent field (CASSCF) calculations. A detailed development of the QMC method leading to the variational QMC (V-QMC) and diffusion QMC (D-QMC) methods is shown. The many-body aspect of electron correlation is introduced into the QMC importance sampling electron-electron correlation functions by using density dependent parameters, and are shown to increase the amount of correlation energy obtained in V-QMC calculations. A detailed analysis of D-QMC time-step bias is made and is found to be at least linear with respect to the time-step. The D-QMC calculations determined the lithium cluster ionization potentials to be 0.1982(14) [0.1981], 0.1895(9) [0.1874(4)], 0.1530(34) [0.1599(73)], 0.1664(37) [0.1724(110)], 0.1613(43) [0.1675(110)] Hartrees for lithium clusters n = 1 through 5, respectively; in good agreement with experimental results shown in the brackets. Also, the binding energies per atom was computed to be 0.0177(8) [0.0203(12)], 0.0188(10) [0.0220(21)], 0.0247(8) [0.0310(12)], 0.0253(8) [0.0351(8)] Hartrees for lithium clusters n = 2 through 5, respectively. The lithium cluster one-electron density is shown to have charge concentrations corresponding to nonnuclear attractors. The overall shape of the electronic charge density also bears a remarkable similarity with the anisotropic harmonic oscillator model shape for the given number of valence electrons.
Monte Carlo study of carrier-light coupling in terahertz quantum cascade lasers
Jirauschek, Christian
2011-01-01
We present a method for self-consistently including the optical cavity field into Monte Carlo-based carrier transport simulations. This approach allows for an analysis of the actual lasing operation in quantum cascade lasers, considering effects such as gain saturation and longitudinal mode competition. Simulation results for a terahertz quantum cascade laser are found to be consistent with experiment.
Monte Carlo simulation of quantum Zeno effect in the brain
Georgiev, Danko
2014-01-01
Environmental decoherence appears to be the biggest obstacle for successful construction of quantum mind theories. Nevertheless, the quantum physicist Henry Stapp promoted the view that the mind could utilize quantum Zeno effect to influence brain dynamics and that the efficacy of such mental efforts would not be undermined by environmental decoherence of the brain. To address the physical plausibility of Stapp's claim, we modeled the brain using quantum tunneling of an electron in a multiple...
Quantum spin models with long-range interactions and tunnelings: a quantum Monte Carlo study
Maik, Michał; Hauke, Philipp; Dutta, Omjyoti; Zakrzewski, Jakub; Lewenstein, Maciej
2012-11-01
We use a quantum Monte Carlo method to investigate various classes of two-dimensional spin models with long-range interactions at low temperatures. In particular, we study a dipolar XXZ model with U(1) symmetry that appears as a hard-core boson limit of an extended Hubbard model describing polarized dipolar atoms or molecules in an optical lattice. Tunneling, in such a model, is short-range, whereas density-density couplings decay with distance following a cubic power law. We also investigate an XXZ model with long-range couplings of all three spin components—such a model describes a system of ultracold ions in a lattice of microtraps. We describe an approximate phase diagram for such systems at zero and at finite temperature, and compare their properties. In particular, we compare the extent of crystalline, superfluid and supersolid phases. Our predictions apply directly to current experiments with mesoscopic numbers of polar molecules and trapped ions.
Cooper, Fred; Dawson, John F.
2016-02-01
We present an alternative to the perturbative (in coupling constant) diagrammatic approach for studying stochastic dynamics of a class of reaction diffusion systems. Our approach is based on an auxiliary field loop expansion for the path integral representation for the generating functional of the noise induced correlation functions of the fields describing these systems. The systems we consider include Langevin systems describable by the set of self interacting classical fields ϕi(x , t) in the presence of external noise ηi(x , t) , namely (∂t - ν∇2) ϕ - F [ ϕ ] = η, as well as chemical reaction annihilation processes obtained by applying the many-body approach of Doi-Peliti to the Master Equation formulation of these problems. We consider two different effective actions, one based on the Onsager-Machlup (OM) approach, and the other due to Janssen-deGenneris based on the Martin-Siggia-Rose (MSR) response function approach. For the simple models we consider, we determine an analytic expression for the Energy landscape (effective potential) in both formalisms and show how to obtain the more physical effective potential of the Onsager-Machlup approach from the MSR effective potential in leading order in the auxiliary field loop expansion. For the KPZ equation we find that our approximation, which is non-perturbative and obeys broken symmetry Ward identities, does not lead to the appearance of a fluctuation induced symmetry breakdown. This contradicts the results of earlier studies.
Confidence and efficiency scaling in Variational Quantum Monte Carlo calculations
Delyon, François; Holzmann, Markus
2016-01-01
Based on the central limit theorem, we discuss the problem of evaluation of the statistical error of Monte Carlo calculations using a time discretized diffusion process. We present a robust and practical method to determine the effective variance of general observables and show how to verify the equilibrium hypothesis by the Kolmogorov-Smirnov test. We then derive scaling laws of the efficiency illustrated by Variational Monte Carlo calculations on the two dimensional electron gas.
Quantum trajectory Monte Carlo method describing the coherent dynamics of highly charged ions
International Nuclear Information System (INIS)
We present a theoretical framework for studying dynamics of open quantum systems. Our formalism gives a systematic path from Hamiltonians constructed by first principles to a Monte Carlo algorithm. Our Monte Carlo calculation can treat the build-up and time evolution of coherences. We employ a reduced density matrix approach in which the total system is divided into a system of interest and its environment. An equation of motion for the reduced density matrix is written in the Lindblad form using an additional approximation to the Born-Markov approximation. The Lindblad form allows the solution of this multi-state problem in terms of Monte Carlo sampling of quantum trajectories. The Monte Carlo method is advantageous in terms of computer storage compared to direct solutions of the equation of motion. We apply our method to discuss coherence properties of the internal state of a Kr35+ ion subject to spontaneous radiative decay. Simulations exhibit clear signatures of coherent transitions
Spin-orbit interactions in electronic structure quantum Monte Carlo methods
Melton, Cody A.; Zhu, Minyi; Guo, Shi; Ambrosetti, Alberto; Pederiva, Francesco; Mitas, Lubos
2016-04-01
We develop generalization of the fixed-phase diffusion Monte Carlo method for Hamiltonians which explicitly depends on particle spins such as for spin-orbit interactions. The method is formulated in a zero-variance manner and is similar to the treatment of nonlocal operators in commonly used static-spin calculations. Tests on atomic and molecular systems show that it is very accurate, on par with the fixed-node method. This opens electronic structure quantum Monte Carlo methods to a vast research area of quantum phenomena in which spin-related interactions play an important role.
Systematic study of finite-size effects in quantum Monte Carlo calculations of real metallic systems
Energy Technology Data Exchange (ETDEWEB)
Azadi, Sam, E-mail: s.azadi@imperial.ac.uk; Foulkes, W. M. C. [Department of Physics, Imperial College London, Exhibition Road, London SW7 2AZ (United Kingdom)
2015-09-14
We present a systematic and comprehensive study of finite-size effects in diffusion quantum Monte Carlo calculations of metals. Several previously introduced schemes for correcting finite-size errors are compared for accuracy and efficiency, and practical improvements are introduced. In particular, we test a simple but efficient method of finite-size correction based on an accurate combination of twist averaging and density functional theory. Our diffusion quantum Monte Carlo results for lithium and aluminum, as examples of metallic systems, demonstrate excellent agreement between all of the approaches considered.
An introduction to applied quantum mechanics in the Wigner Monte Carlo formalism
International Nuclear Information System (INIS)
The Wigner formulation of quantum mechanics is a very intuitive approach which allows the comprehension and prediction of quantum mechanical phenomena in terms of quasi-distribution functions. In this review, our aim is to provide a detailed introduction to this theory along with a Monte Carlo method for the simulation of time-dependent quantum systems evolving in a phase-space. This work consists of three main parts. First, we introduce the Wigner formalism, then we discuss in detail the Wigner Monte Carlo method and, finally, we present practical applications. In particular, the Wigner model is first derived from the Schrödinger equation. Then a generalization of the formalism due to Moyal is provided, which allows to recover important mathematical properties of the model. Next, the Wigner equation is further generalized to the case of many-body quantum systems. Finally, a physical interpretation of the negative part of a quasi-distribution function is suggested. In the second part, the Wigner Monte Carlo method, based on the concept of signed (virtual) particles, is introduced in detail for the single-body problem. Two extensions of the Wigner Monte Carlo method to quantum many-body problems are introduced, in the frameworks of time-dependent density functional theory and ab-initio methods. Finally, in the third and last part of this paper, applications to single- and many-body problems are performed in the context of quantum physics and quantum chemistry, specifically focusing on the hydrogen, lithium and boron atoms, the H2 molecule and a system of two identical Fermions. We conclude this work with a discussion on the still unexplored directions the Wigner Monte Carlo method could take in the next future
An introduction to applied quantum mechanics in the Wigner Monte Carlo formalism
Energy Technology Data Exchange (ETDEWEB)
Sellier, J.M., E-mail: jeanmichel.sellier@parallel.bas.bg [IICT, Bulgarian Academy of Sciences, Acad. G. Bonchev str. 25A, 1113 Sofia (Bulgaria); Nedjalkov, M. [IICT, Bulgarian Academy of Sciences, Acad. G. Bonchev str. 25A, 1113 Sofia (Bulgaria); Institute for Microelectronics, TU Wien, Gußhausstraße 27-29/E360, 1040 Wien (Austria); Dimov, I. [IICT, Bulgarian Academy of Sciences, Acad. G. Bonchev str. 25A, 1113 Sofia (Bulgaria)
2015-05-12
The Wigner formulation of quantum mechanics is a very intuitive approach which allows the comprehension and prediction of quantum mechanical phenomena in terms of quasi-distribution functions. In this review, our aim is to provide a detailed introduction to this theory along with a Monte Carlo method for the simulation of time-dependent quantum systems evolving in a phase-space. This work consists of three main parts. First, we introduce the Wigner formalism, then we discuss in detail the Wigner Monte Carlo method and, finally, we present practical applications. In particular, the Wigner model is first derived from the Schrödinger equation. Then a generalization of the formalism due to Moyal is provided, which allows to recover important mathematical properties of the model. Next, the Wigner equation is further generalized to the case of many-body quantum systems. Finally, a physical interpretation of the negative part of a quasi-distribution function is suggested. In the second part, the Wigner Monte Carlo method, based on the concept of signed (virtual) particles, is introduced in detail for the single-body problem. Two extensions of the Wigner Monte Carlo method to quantum many-body problems are introduced, in the frameworks of time-dependent density functional theory and ab-initio methods. Finally, in the third and last part of this paper, applications to single- and many-body problems are performed in the context of quantum physics and quantum chemistry, specifically focusing on the hydrogen, lithium and boron atoms, the H{sub 2} molecule and a system of two identical Fermions. We conclude this work with a discussion on the still unexplored directions the Wigner Monte Carlo method could take in the next future.
Grover search algorithm with Rydberg-blockaded atoms: quantum Monte Carlo simulations
Petrosyan, David; Saffman, Mark; Mølmer, Klaus
2016-05-01
We consider the Grover search algorithm implementation for a quantum register of size N={2}k using k (or k+1) microwave- and laser-driven Rydberg-blockaded atoms, following the proposal by Mølmer et al (2011 J. Phys. B 44 184016). We suggest some simplifications for the microwave and laser couplings, and analyze the performance of the algorithm for up to k = 4 multilevel atoms under realistic experimental conditions using quantum stochastic (Monte Carlo) wavefunction simulations.
Monte Carlo simulation of hot-carrier phenomena in open quantum devices: A kinetic approach
Rossi, Fausto; Proietti Zaccaria, Remo; Iotti, Rita Claudia
2004-01-01
An alternative simulation strategy for the study of nonequilibrium carrier dynamics in quantum devices with open boundaries is presented. In particular, we propose replacing the usual modeling of open quantum systems based on phenomenological injection/loss rates with a kinetic description of the system-reservoir thermalization process. More specifically, in this simulation scheme the partial carrier thermalization induced by the device spatial boundaries is treated within the standard Monte ...
Quantum Monte Carlo Simulations of Adulteration Effect on Bond Alternating Spin=1/2 Chain
Zhang, Peng; Xu, Zhaoxin; Ying, Heping; Dai, Jianhui; Crompton, Peter
The S=1/2 Heisenberg chain with bond alternation and randomness of antiferromagnetic (AFM) and ferromagnetic (FM) interactions is investigated by quantum Monte Carlo simulations of loop/cluster algorithm. Our results have shown interesting finite temperature magnetic properties of this model. The relevance of our study to former investigation results is discussed.
Improved Green’s function measurement for hybridization expansion quantum Monte Carlo
Czech Academy of Sciences Publication Activity Database
Augustinský, Pavel; Kuneš, Jan
2013-01-01
Roč. 184, č. 9 (2013), s. 2119-2126. ISSN 0010-4655 Institutional support: RVO:68378271 Keywords : continuous time quantum Monte Carlo method * Green function estimator Subject RIV: BE - Theoretical Physics Impact factor: 2.407, year: 2013
Stability of few-body systems and quantum Monte-Carlo methods
International Nuclear Information System (INIS)
Quantum Monte-Carlo methods are well suited to study the stability of few-body systems. Their capabilities are illustrated by studying the critical stability of the hydrogen molecular ion whose nuclei and electron interact through the Yukawa potential, and the stability of small helium clusters. Refs. 16 (author)
Quantum Monte Carlo study of spin-polarized deuterium
Beslic, I.; Markic, L. Vranjes; Casulleras, J.; Boronat, J.
2012-01-01
The ground state properties of spin-polarized deuterium (D$\\downarrow$) at zero temperature are obtained by means of the diffusion Monte Carlo calculations within the fixed-node approximation. Three D$\\downarrow$ species have been investigated (D$\\downarrow_1$, D$\\downarrow_2$, D$\\downarrow_3$), corresponding respectively to one, two and three equally occupied nuclear spin states. Influence of the backflow correlations on the ground state energy of the systems is explored. The equilibrium den...
Communication: Variation after response in quantum Monte Carlo.
Neuscamman, Eric
2016-08-28
We present a new method for modeling electronically excited states that overcomes a key failing of linear response theory by allowing the underlying ground state ansatz to relax in the presence of an excitation. The method is variational, has a cost similar to ground state variational Monte Carlo, and admits both open and periodic boundary conditions. We present preliminary numerical results showing that, when paired with the Jastrow antisymmetric geminal power ansatz, the variation-after-response formalism delivers accuracies for valence and charge transfer single excitations on par with equation of motion coupled cluster, while surpassing coupled cluster's accuracy for excitations with significant doubly excited character. PMID:27586897
CPMC-Lab: A MATLAB package for Constrained Path Monte Carlo calculations
Nguyen, Huy; Shi, Hao; Xu, Jie; Zhang, Shiwei
2014-12-01
We describe CPMC-Lab, a MATLAB program for the constrained-path and phaseless auxiliary-field Monte Carlo methods. These methods have allowed applications ranging from the study of strongly correlated models, such as the Hubbard model, to ab initio calculations in molecules and solids. The present package implements the full ground-state constrained-path Monte Carlo (CPMC) method in MATLAB with a graphical interface, using the Hubbard model as an example. The package can perform calculations in finite supercells in any dimensions, under periodic or twist boundary conditions. Importance sampling and all other algorithmic details of a total energy calculation are included and illustrated. This open-source tool allows users to experiment with various model and run parameters and visualize the results. It provides a direct and interactive environment to learn the method and study the code with minimal overhead for setup. Furthermore, the package can be easily generalized for auxiliary-field quantum Monte Carlo (AFQMC) calculations in many other models for correlated electron systems, and can serve as a template for developing a production code for AFQMC total energy calculations in real materials. Several illustrative studies are carried out in one- and two-dimensional lattices on total energy, kinetic energy, potential energy, and charge- and spin-gaps.
Giner, Emmanuel; Toulouse, Julien
2016-01-01
We explore the use in quantum Monte Carlo (QMC) of trial wave functions consisting of a Jastrow factor multiplied by a truncated configuration-interaction (CI) expansion in Slater determinants obtained from a CI perturbatively selected iteratively (CIPSI) calculation. In the CIPSI algorithm, the CI expansion is iteratively enlarged by selecting the best determinants using perturbation theory, which provides an optimal and automatic way of constructing truncated CI expansions approaching the full CI limit. We perform a systematic study of variational Monte Carlo (VMC) and fixed-node diffusion Monte Carlo (DMC) total energies of first-row atoms from B to Ne with different levels of optimization of the parameters (Jastrow parameters, coefficients of the determinants, and orbital parameters) in these trial wave functions. The results show that the reoptimization of the coefficients of the determinants in VMC (together with the Jastrow factor) leads to an important lowering of both VMC and DMC total energies, and ...
Overy, Catherine; Blunt, N S; Shepherd, James; Cleland, Deidre; Alavi, Ali
2014-01-01
Properties that are necessarily formulated within pure (symmetric) expectation values are difficult to calculate for projector quantum Monte Carlo approaches, but are critical in order to compute many of the important observable properties of electronic systems. Here, we investigate an approach for the sampling of unbiased reduced density matrices within the Full Configuration Interaction Quantum Monte Carlo dynamic, which requires only small computational overheads. This is achieved via an independent replica population of walkers in the dynamic, sampled alongside the original population. The resulting reduced density matrices are free from systematic error (beyond those present via constraints on the dynamic itself), and can be used to compute a variety of expectation values and properties, with rapid convergence to an exact limit. A quasi-variational energy estimate derived from these density matrices is proposed as an accurate alternative to the projected estimator for multiconfigurational wavefunctions, ...
Charged vanadium-benzene multidecker clusters: DFT and quantum Monte Carlo study.
Tokár, K; Derian, R; Mitas, L; Štich, I
2016-02-14
Using explicitly correlated fixed-node quantum Monte Carlo and density functional theory (DFT) methods, we study electronic properties, ground-state multiplets, ionization potentials, electron affinities, and low-energy fragmentation channels of charged half-sandwich and multidecker vanadium-benzene systems with up to 3 vanadium atoms, including both anions and cations. It is shown that, particularly in anions, electronic correlations play a crucial role; these effects are not systematically captured with any commonly used DFT functionals such as gradient corrected, hybrids, and range-separated hybrids. On the other hand, tightly bound cations can be described qualitatively by DFT. A comparison of DFT and quantum Monte Carlo provides an in-depth understanding of the electronic structure and properties of these correlated systems. The calculations also serve as a benchmark study of 3d molecular anions that require a balanced many-body description of correlations at both short- and long-range distances. PMID:26874484
Charged vanadium-benzene multidecker clusters: DFT and quantum Monte Carlo study
Tokár, K.; Derian, R.; Mitas, L.; Štich, I.
2016-02-01
Using explicitly correlated fixed-node quantum Monte Carlo and density functional theory (DFT) methods, we study electronic properties, ground-state multiplets, ionization potentials, electron affinities, and low-energy fragmentation channels of charged half-sandwich and multidecker vanadium-benzene systems with up to 3 vanadium atoms, including both anions and cations. It is shown that, particularly in anions, electronic correlations play a crucial role; these effects are not systematically captured with any commonly used DFT functionals such as gradient corrected, hybrids, and range-separated hybrids. On the other hand, tightly bound cations can be described qualitatively by DFT. A comparison of DFT and quantum Monte Carlo provides an in-depth understanding of the electronic structure and properties of these correlated systems. The calculations also serve as a benchmark study of 3d molecular anions that require a balanced many-body description of correlations at both short- and long-range distances.
Charged vanadium-benzene multidecker clusters: DFT and quantum Monte Carlo study
International Nuclear Information System (INIS)
Using explicitly correlated fixed-node quantum Monte Carlo and density functional theory (DFT) methods, we study electronic properties, ground-state multiplets, ionization potentials, electron affinities, and low-energy fragmentation channels of charged half-sandwich and multidecker vanadium-benzene systems with up to 3 vanadium atoms, including both anions and cations. It is shown that, particularly in anions, electronic correlations play a crucial role; these effects are not systematically captured with any commonly used DFT functionals such as gradient corrected, hybrids, and range-separated hybrids. On the other hand, tightly bound cations can be described qualitatively by DFT. A comparison of DFT and quantum Monte Carlo provides an in-depth understanding of the electronic structure and properties of these correlated systems. The calculations also serve as a benchmark study of 3d molecular anions that require a balanced many-body description of correlations at both short- and long-range distances
Charged vanadium-benzene multidecker clusters: DFT and quantum Monte Carlo study
Energy Technology Data Exchange (ETDEWEB)
Tokár, K.; Derian, R. [Institute of Physics, CCMS, Slovak Academy of Sciences, 84511 Bratislava (Slovakia); Mitas, L. [Department of Physics, North Carolina State University, Raleigh, North Carolina 27695-8202 (United States); Štich, I., E-mail: ivan.stich@savba.sk [Institute of Physics, CCMS, Slovak Academy of Sciences, 84511 Bratislava (Slovakia); Ruprecht A. Institute of Technology, Bratislava (Slovakia)
2016-02-14
Using explicitly correlated fixed-node quantum Monte Carlo and density functional theory (DFT) methods, we study electronic properties, ground-state multiplets, ionization potentials, electron affinities, and low-energy fragmentation channels of charged half-sandwich and multidecker vanadium-benzene systems with up to 3 vanadium atoms, including both anions and cations. It is shown that, particularly in anions, electronic correlations play a crucial role; these effects are not systematically captured with any commonly used DFT functionals such as gradient corrected, hybrids, and range-separated hybrids. On the other hand, tightly bound cations can be described qualitatively by DFT. A comparison of DFT and quantum Monte Carlo provides an in-depth understanding of the electronic structure and properties of these correlated systems. The calculations also serve as a benchmark study of 3d molecular anions that require a balanced many-body description of correlations at both short- and long-range distances.
Role of Electronic Correlation in the Si(100) Reconstruction: A Quantum Monte Carlo Study
Energy Technology Data Exchange (ETDEWEB)
Healy, Sorcha B.; Filippi, Claudia; Kratzer, P.; Penev, E.; Scheffler, M.
2001-07-02
Recent low-temperature scanning tunneling experiments have questioned the generally accepted picture of buckled silicon dimers as the ground state reconstruction of the Si(100) surface, undermining the ability of density functional theory to accurately describe electronic correlations at surfaces. We present quantum Monte Carlo calculations on large cluster models of the surface, and conclude that buckling remains energetically favorable even when the present-day best treatment of electronic correlation is employed. The implications for experimental interpretation are discussed.
Jirauschek, Christian; Okeil, Hesham; Lugli, Paolo
2015-01-26
Based on self-consistent ensemble Monte Carlo simulations coupled to the optical field dynamics, we investigate the giant nonlinear susceptibility giving rise to terahertz difference frequency generation in quantum cascade laser structures. Specifically, the dependence on temperature, bias voltage and frequency is considered. It is shown that the optical nonlinearity is temperature insensitive and covers a broad spectral range, as required for widely tunable room temperature terahertz sources. The obtained results are consistent with available experimental data. PMID:25835923
Seth, Priyanka; Krivenko, Igor; Ferrero, Michel; Parcollet, Olivier
2016-03-01
We present TRIQS/CTHYB, a state-of-the art open-source implementation of the continuous-time hybridisation expansion quantum impurity solver of the TRIQS package. This code is mainly designed to be used with the TRIQS library in order to solve the self-consistent quantum impurity problem in a multi-orbital dynamical mean field theory approach to strongly-correlated electrons, in particular in the context of realistic electronic structure calculations. It is implemented in C++ for efficiency and is provided with a high-level Python interface. The code ships with a new partitioning algorithm that divides the local Hilbert space without any user knowledge of the symmetries and quantum numbers of the Hamiltonian. Furthermore, we implement higher-order configuration moves and show that such moves are necessary to ensure ergodicity of the Monte Carlo in common Hamiltonians even without symmetry-breaking.
Introducing QMC/MMpol: Quantum Monte Carlo in Polarizable Force Fields for Excited States.
Guareschi, Riccardo; Zulfikri, Habiburrahman; Daday, Csaba; Floris, Franca Maria; Amovilli, Claudio; Mennucci, Benedetta; Filippi, Claudia
2016-04-12
We present for the first time a quantum mechanics/molecular mechanics scheme which combines quantum Monte Carlo with the reaction field of classical polarizable dipoles (QMC/MMpol). In our approach, the optimal dipoles are self-consistently generated at the variational Monte Carlo level and then used to include environmental effects in diffusion Monte Carlo. We investigate the performance of this hybrid model in describing the vertical excitation energies of prototypical small molecules solvated in water, namely, methylenecyclopropene and s-trans acrolein. Two polarization regimes are explored where either the dipoles are optimized with respect to the ground-state solute density (polGS) or different sets of dipoles are separately brought to equilibrium with the states involved in the electronic transition (polSS). By comparing with reference supermolecular calculations where both solute and solvent are treated quantum mechanically, we find that the inclusion of the response of the environment to the excitation of the solute leads to superior results than the use of a frozen environment (point charges or polGS), in particular, when the solute-solvent coupling is dominated by electrostatic effects which are well recovered in the polSS condition. QMC/MMpol represents therefore a robust scheme to treat important environmental effects beyond static point charges, combining the accuracy of QMC with the simplicity of a classical approach. PMID:26959751
Quantum Monte Carlo algorithms for electronic structure at the petascale; the endstation project.
Energy Technology Data Exchange (ETDEWEB)
Kim, J; Ceperley, D M; Purwanto, W; Walter, E J; Krakauer, H; Zhang, S W; Kent, P.R. C; Hennig, R G; Umrigar, C; Bajdich, M; Kolorenc, J; Mitas, L
2008-10-01
Over the past two decades, continuum quantum Monte Carlo (QMC) has proved to be an invaluable tool for predicting of the properties of matter from fundamental principles. By solving the Schrodinger equation through a stochastic projection, it achieves the greatest accuracy and reliability of methods available for physical systems containing more than a few quantum particles. QMC enjoys scaling favorable to quantum chemical methods, with a computational effort which grows with the second or third power of system size. This accuracy and scalability has enabled scientific discovery across a broad spectrum of disciplines. The current methods perform very efficiently at the terascale. The quantum Monte Carlo Endstation project is a collaborative effort among researchers in the field to develop a new generation of algorithms, and their efficient implementations, which will take advantage of the upcoming petaflop architectures. Some aspects of these developments are discussed here. These tools will expand the accuracy, efficiency and range of QMC applicability and enable us to tackle challenges which are currently out of reach. The methods will be applied to several important problems including electronic and structural properties of water, transition metal oxides, nanosystems and ultracold atoms.
Sign learning kink-based (SiLK) quantum Monte Carlo for molecular systems
Ma, Xiaoyao; Loffler, Frank; Kowalski, Karol; Bhaskaran-Nair, Kiran; Jarrell, Mark; Moreno, Juana
2015-01-01
The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used to calculate the ab initio ground state energies for multiple geometries of the H$_{2}$O, N$_2$, and F$_2$ molecules. The method is based on Feynman's path integral formulation of quantum mechanics and has two stages. The first stage is called the learning stage and reduces the well-known QMC minus sign problem by optimizing the linear combinations of Slater determinants which are used in the second stage, a conventional QMC simulation. The method is tested using different vector spaces and compared to the results of other quantum chemical methods and to exact diagonalization. Our findings demonstrate that the SiLK method is accurate and reduces or eliminates the minus sign problem.
Sign Learning Kink-based (SiLK) Quantum Monte Carlo for molecular systems.
Ma, Xiaoyao; Hall, Randall W; Löffler, Frank; Kowalski, Karol; Bhaskaran-Nair, Kiran; Jarrell, Mark; Moreno, Juana
2016-01-01
The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used to calculate the ab initio ground state energies for multiple geometries of the H2O, N2, and F2 molecules. The method is based on Feynman's path integral formulation of quantum mechanics and has two stages. The first stage is called the learning stage and reduces the well-known QMC minus sign problem by optimizing the linear combinations of Slater determinants which are used in the second stage, a conventional QMC simulation. The method is tested using different vector spaces and compared to the results of other quantum chemical methods and to exact diagonalization. Our findings demonstrate that the SiLK method is accurate and reduces or eliminates the minus sign problem. PMID:26747795
Sign Learning Kink-based (SiLK) Quantum Monte Carlo for molecular systems
Ma, Xiaoyao; Hall, Randall W.; Löffler, Frank; Kowalski, Karol; Bhaskaran-Nair, Kiran; Jarrell, Mark; Moreno, Juana
2016-01-01
The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used to calculate the ab initio ground state energies for multiple geometries of the H2O, N2, and F2 molecules. The method is based on Feynman's path integral formulation of quantum mechanics and has two stages. The first stage is called the learning stage and reduces the well-known QMC minus sign problem by optimizing the linear combinations of Slater determinants which are used in the second stage, a conventional QMC simulation. The method is tested using different vector spaces and compared to the results of other quantum chemical methods and to exact diagonalization. Our findings demonstrate that the SiLK method is accurate and reduces or eliminates the minus sign problem.
Sign learning kink-based (SiLK) quantum Monte Carlo for molecular systems
Energy Technology Data Exchange (ETDEWEB)
Ma, Xiaoyao; Hall, Randall W.; Loffler, Frank; Kowalski, Karol; Bhaskaran-Nair, Kiran; Jarrell, Mark; Moreno, Juana
2016-01-07
The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used to calculate the ab initio ground state energies for multiple geometries of the H2O, N2, and F2 molecules. The method is based on Feynman’s path integral formulation of quantum mechanics and has two stages. The first stage is called the learning stage and reduces the well-known QMC minus sign problem by optimizing the linear combinations of Slater determinants which are used in the second stage, a conventional QMC simulation. The method is tested using different vector spaces and compared to the results of other quantum chemical methods and to exact diagonalization. Our findings demonstrate that the SiLK method is accurate and reduces or eliminates the minus sign problem.
Sign Learning Kink-based (SiLK) Quantum Monte Carlo for molecular systems
Energy Technology Data Exchange (ETDEWEB)
Ma, Xiaoyao [Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803 (United States); Hall, Randall W. [Department of Natural Sciences and Mathematics, Dominican University of California, San Rafael, California 94901 (United States); Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803 (United States); Löffler, Frank [Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803 (United States); Kowalski, Karol [William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, Richland, Washington 99352 (United States); Bhaskaran-Nair, Kiran; Jarrell, Mark; Moreno, Juana [Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803 (United States); Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803 (United States)
2016-01-07
The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used to calculate the ab initio ground state energies for multiple geometries of the H{sub 2}O, N{sub 2}, and F{sub 2} molecules. The method is based on Feynman’s path integral formulation of quantum mechanics and has two stages. The first stage is called the learning stage and reduces the well-known QMC minus sign problem by optimizing the linear combinations of Slater determinants which are used in the second stage, a conventional QMC simulation. The method is tested using different vector spaces and compared to the results of other quantum chemical methods and to exact diagonalization. Our findings demonstrate that the SiLK method is accurate and reduces or eliminates the minus sign problem.
Sign Learning Kink-based (SiLK) Quantum Monte Carlo for molecular systems
International Nuclear Information System (INIS)
The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used to calculate the ab initio ground state energies for multiple geometries of the H2O, N2, and F2 molecules. The method is based on Feynman’s path integral formulation of quantum mechanics and has two stages. The first stage is called the learning stage and reduces the well-known QMC minus sign problem by optimizing the linear combinations of Slater determinants which are used in the second stage, a conventional QMC simulation. The method is tested using different vector spaces and compared to the results of other quantum chemical methods and to exact diagonalization. Our findings demonstrate that the SiLK method is accurate and reduces or eliminates the minus sign problem
International Nuclear Information System (INIS)
We present a new form of explicitly correlated wavefunction whose parameters are mainly linear, to circumvent the problem of the optimization of a large number of nonlinear parameters usually encountered with basis sets of explicitly correlated wavefunctions. With this trial wavefunction we have succeeded in minimizing the energy instead of the variance of the local energy, as is more common in quantum Monte Carlo methods. We have applied this wavefunction to the calculation of the energies of Be 3P (1s22p2) and Be-4So (1s22p3) by variational and diffusion Monte Carlo methods. The results compare favourably with those obtained by different types of explicitly correlated trial wavefunction already described in the literature. The energies obtained are improved with respect to the best variational ones found in the literature, and within one standard deviation of the estimated non-relativistic limits. (author)
Renormalization group studies and Monte Carlo simulation for quantum spin systems
International Nuclear Information System (INIS)
Extended application of various real-space renormalization group methods to quantum spin systems is discussed. At finite temperature, both the reliability and range of application of the decimation renormalization group method (DRG) are extended for calculating the thermal and magnetic properties of low-dimensional quantum spin chains, in which general models of the three-state Potts model and the general Heisenberg model are proposed. Some interesting finite-temperature behavior of the models was obtained. Also proposed is a general formula for the critical properties of the n-dimensional q-state Potts model by using a modified Migdal-Kadanoff approach which is in very good agreement with all available results for general q and d. For high-spin systems, the famous Haldane's prediction was studied by using a modified block renormalization group approach in spin-1/2, spin-1, and spin-3/2 cases. The results supports Haldane's prediction and a novel property of the spin-1 Heisenberg antiferromagnet has been predicted. A modified quantum Monte Carlo simulation approach was developed in this study and used to treat quantum interacting problems (only quantum spin systems are studied) without the negative sign problem
Calcavecchia, Francesco; Holzmann, Markus
2016-04-01
We use the shadow wave function formalism as a convenient model to study the fermion sign problem affecting all projector quantum Monte Carlo methods in continuum space. We demonstrate that the efficiency of imaginary-time projection algorithms decays exponentially with increasing number of particles and/or imaginary-time propagation. Moreover, we derive an analytical expression that connects the localization of the system with the magnitude of the sign problem, illustrating this behavior through numerical results. Finally, we discuss the computational complexity of the fermion sign problem and methods for alleviating its severity.
Neutron matter with Quantum Monte Carlo: chiral 3N forces and static response
Buraczynski, M.; Gandolfi, S.; Gezerlis, A.; Schwenk, A.; Tews, I.
2016-03-01
Neutron matter is related to the physics of neutron stars and that of neutron-rich nuclei. Quantum Monte Carlo (QMC) methods offer a unique way of solving the many-body problem non-perturbatively, providing feedback on features of nuclear interactions and addressing scenarios that are inaccessible to other approaches. In this contribution we go over two recent accomplishments in the theory of neutron matter: a) the fusing of QMC with chiral effective field theory interactions, focusing on local chiral 3N forces, and b) the first attempt to find an ab initio solution to the problem of static response.
Integration of the adjoint gamma quantum transport equation by the Monte Carlo method
International Nuclear Information System (INIS)
Comparative description and analysis of the direct and adjoint algorithms of calculation of gamma-quantum transmission in shielding using the Monte Carlo method have been carried out. Adjoint estimations for a number of monoenergetic sources have been considered. A brief description of ''COMETA'' program for BESM-6 computer reazaling direct and adjoint algorithms is presented. The program is modular-constructed which allows to widen it the new module-units being joined. Results of solution by the adjoint branch of two analog problems as compared to the analytical data are presented. These results confirm high efficiency of ''COMETA'' program
A study of potential energy curves from the model space quantum Monte Carlo method
Energy Technology Data Exchange (ETDEWEB)
Ohtsuka, Yuhki; Ten-no, Seiichiro, E-mail: tenno@cs.kobe-u.ac.jp [Department of Computational Sciences, Graduate School of System Informatics, Kobe University, Nada-ku, Kobe 657-8501 (Japan)
2015-12-07
We report on the first application of the model space quantum Monte Carlo (MSQMC) to potential energy curves (PECs) for the excited states of C{sub 2}, N{sub 2}, and O{sub 2} to validate the applicability of the method. A parallel MSQMC code is implemented with the initiator approximation to enable efficient sampling. The PECs of MSQMC for various excited and ionized states are compared with those from the Rydberg-Klein-Rees and full configuration interaction methods. The results indicate the usefulness of MSQMC for precise PECs in a wide range obviating problems concerning quasi-degeneracy.
A Monte Carlo-quantum mechanics study of a solvatochromic π* probe.
Domínguez, Moisés; Rezende, Marcos Caroli
2016-09-01
The solvation and the solvatochromic behavior of 5-(dimethylamino)-5'-nitro-2,2'-bithiophene 1, the basis of a π* scale of solvent polarities, was investigated theoretically in toluene, dichloromethane, methanol and formamide with a Monte Carlo and quantum mechanics (QM/MM) iterative approach. The calculated transition energies of the solvatochromic band of 1, obtained as averages of statistically uncorrelated configurations, including the solute and explicit solvent molecules of the first solvation layer, besides showing good agreement with the experimental transitions, reproduced very well the positive solvatochromism of this probe in various solvents. PMID:27553303
Chiral 2N and 3N interactions and quantum Monte Carlo applications
Directory of Open Access Journals (Sweden)
Gezerlis Alexandros
2016-01-01
Full Text Available Chiral Effective Field Theory (EFT two- and three-nucleon forces are now widely employed. Since they were originally formulated in momentum space, these interactions were non-local, making them inaccessible to Quantum Monte Carlo (QMC methods. We have recently derived a local version of chiral EFT nucleon-nucleon and three-nucleon interactions, which we also used in QMC calculations for neutron matter and light nuclei. In this contribution I go over the basics of local chiral EFT and then summarize recent results.
Anagnostopoulos, Konstantinos N; Hanada, Masanori; Nishimura, Jun; Takeuchi, Shingo
2008-01-18
We present the first Monte Carlo results for supersymmetric matrix quantum mechanics with 16 supercharges at finite temperature. The recently proposed nonlattice simulation enables us to include the effects of fermionic matrices in a transparent and reliable manner. The internal energy nicely interpolates the weak coupling behavior obtained by the high temperature expansion, and the strong coupling behavior predicted from the dual black-hole geometry. The Polyakov line asymptotes at low temperature to a characteristic behavior for a deconfined theory, suggesting the absence of a phase transition. These results provide highly nontrivial evidence for the gauge-gravity duality. PMID:18232852
Theory of Finite Size Effects for Electronic Quantum Monte Carlo Calculations of Liquids and Solids
Holzmann, Markus; Morales, Miguel A; Tubmann, Norm M; Ceperley, David M; Pierleoni, Carlo
2016-01-01
Concentrating on zero temperature Quantum Monte Carlo calculations of electronic systems, we give a general description of the theory of finite size extrapolations of energies to the thermodynamic limit based on one and two-body correlation functions. We introduce new effective procedures, such as using the potential and wavefunction split-up into long and short range functions to simplify the method and we discuss how to treat backflow wavefunctions. Then we explicitly test the accuracy of our method to correct finite size errors on example hydrogen and helium many-body systems and show that the finite size bias can be drastically reduced for even small systems.
Optimization of Quantum Monte Carlo Wave Functions Using Analytical Energy Derivatives
Lin, X; Rappe, A M; Lin, Xi; Zhang, Hongkai; Rappe, Andrew M.
1999-01-01
An algorithm is proposed to optimize quantum Monte Carlo (QMC) wave functions based on New ton's method and analytical computation of the first and second derivatives of the variati onal energy. This direct application of the variational principle yields significantly low er energy than variance minimization methods when applied to the same trial wave function. Quadratic convergence to the local minimum of the variational parameters is achieved. A g eneral theorem is presented, which substantially simplifies the analytic expressions of de rivatives in the case of wave function optimization. To demonstrate the method, the ground state energies of the first-row elements are calculated.
Constraining the nuclear energy density functional with quantum Monte Carlo calculations
Roggero, Alessandro; Mukherjee, Abhishek; Pederiva, Francesco
2014-01-01
We study the problem of an impurity in fully polarized (spin-up) low density neutron matter with the help of an accurate quantum Monte Carlo method in conjunction with a realistic nucleon-nucleon interaction derived from chiral effective field theory at next-to-next-to-leading-order. Our calculations show that the behavior of the proton spin-down impurity is very similar to that of a polaron in a fully polarized unitary Fermi gas. We show that our results can be used to put tight constraints ...
International Nuclear Information System (INIS)
We present the first Monte Carlo results for supersymmetric matrix quantum mechanics with 16 supercharges at finite temperature. The recently proposed nonlattice simulation enables us to include the effects of fermionic matrices in a transparent and reliable manner. The internal energy nicely interpolates the weak coupling behavior obtained by the high temperature expansion, and the strong coupling behavior predicted from the dual black-hole geometry. The Polyakov line asymptotes at low temperature to a characteristic behavior for a deconfined theory, suggesting the absence of a phase transition. These results provide highly nontrivial evidence for the gauge-gravity duality
Quantum Monte Carlo simulation of suprafluidity with fermions in a two dimensional optical lattice
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Based on a Projector Quantum Monte Carlo Simulation, we examine the ground state properties of the attractive 2D fermionic Hubbard model. The main focus is on the supersolid phase, where in a periodic system it is known that the superfluid phase coexists with a crystalline structure (CDW-phase) at density n=1. We obtain the conditions for such a phase when the system is confined in a harmonic trap. Furthermore, we consider the BCS-BEC crossover region in a periodic system.
Ab initio molecular dynamics simulation of liquid water by quantum Monte Carlo
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Although liquid water is ubiquitous in chemical reactions at roots of life and climate on the earth, the prediction of its properties by high-level ab initio molecular dynamics simulations still represents a formidable task for quantum chemistry. In this article, we present a room temperature simulation of liquid water based on the potential energy surface obtained by a many-body wave function through quantum Monte Carlo (QMC) methods. The simulated properties are in good agreement with recent neutron scattering and X-ray experiments, particularly concerning the position of the oxygen-oxygen peak in the radial distribution function, at variance of previous density functional theory attempts. Given the excellent performances of QMC on large scale supercomputers, this work opens new perspectives for predictive and reliable ab initio simulations of complex chemical systems
Ab-initio molecular dynamics simulation of liquid water by Quantum Monte Carlo
Zen, Andrea; Mazzola, Guglielmo; Guidoni, Leonardo; Sorella, Sandro
2014-01-01
Despite liquid water is ubiquitous in chemical reactions at roots of life and climate on earth, the prediction of its properties by high-level ab initio molecular dynamics simulations still represents a formidable task for quantum chemistry. In this article we present a room temperature simulation of liquid water based on the potential energy surface obtained by a many-body wave function through quantum Monte Carlo (QMC) methods. The simulated properties are in excellent agreement with recent neutron scattering and X-ray experiments, particularly concerning the position of the oxygen-oxygen peak in the radial distribution function, at variance of previous Density Functional Theory attempts. Given the excellent performances of QMC on large scale supercomputers, this work opens new perspectives for predictive and reliable ab-initio simulations of complex chemical systems.
Ab initio molecular dynamics simulation of liquid water by quantum Monte Carlo
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Zen, Andrea, E-mail: a.zen@ucl.ac.uk [Dipartimento di Fisica, “La Sapienza” - Università di Roma, piazzale Aldo Moro 5, 00185 Rome (Italy); London Centre for Nanotechnology, University College London, London WC1E 6BT (United Kingdom); Luo, Ye, E-mail: xw111luoye@gmail.com; Mazzola, Guglielmo, E-mail: gmazzola@phys.ethz.ch; Sorella, Sandro, E-mail: sorella@sissa.it [SISSA–International School for Advanced Studies, Via Bonomea 26, 34136 Trieste (Italy); Democritos Simulation Center CNR–IOM Istituto Officina dei Materiali, 34151 Trieste (Italy); Guidoni, Leonardo, E-mail: leonardo.guidoni@univaq.it [Dipartimento di Fisica, “La Sapienza” - Università di Roma, piazzale Aldo Moro 5, 00185 Rome (Italy); Dipartimento di Scienze Fisiche e Chimiche, Università degli Studi dell’ Aquila, via Vetoio, 67100 L’ Aquila (Italy)
2015-04-14
Although liquid water is ubiquitous in chemical reactions at roots of life and climate on the earth, the prediction of its properties by high-level ab initio molecular dynamics simulations still represents a formidable task for quantum chemistry. In this article, we present a room temperature simulation of liquid water based on the potential energy surface obtained by a many-body wave function through quantum Monte Carlo (QMC) methods. The simulated properties are in good agreement with recent neutron scattering and X-ray experiments, particularly concerning the position of the oxygen-oxygen peak in the radial distribution function, at variance of previous density functional theory attempts. Given the excellent performances of QMC on large scale supercomputers, this work opens new perspectives for predictive and reliable ab initio simulations of complex chemical systems.
Low-pressure phase diagram of crystalline benzene from quantum Monte Carlo
Azadi, Sam
2016-01-01
We study the low-pressure (0 to 10 GPa) phase diagram of crystalline benzene using quantum Monte Carlo (QMC) and density functional theory (DFT) methods. We consider the $Pbca$, $P4_32_12$, and $P2_1/c$ structures as the best candidates for phase I and phase II. We perform diffusion quantum Monte Carlo (DMC) calculations to obtain accurate static phase diagrams as benchmarks for modern van der Waals density functionals. We use density functional perturbation theory to compute phonon contribution in the free-energy calculations. Our DFT enthalpy-pressure phase diagram indicates that the $Pbca$ and $P2_1/c$ structures are the most stable phases within the studied pressure range. The DMC Gibbs free-energy calculations predict that the room temperature $Pbca$ to $P2_1/c$ phase transition occurs at 2.1(1) GPa. This prediction is consistent with available experimental results at room temperature. Our DMC calculations show an estimate of 50.6$\\pm$0.5 kJ/mol for crystalline benzene lattice energy.
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Although the leading-order scaling of entanglement entropy is non-universal at a quantum critical point (QCP), sub-leading scaling can contain universal behaviour. Such universal quantities are commonly studied in non-interacting field theories, however it typically requires numerical calculation to access them in interacting theories. In this paper, we use large-scale T = 0 quantum Monte Carlo simulations to examine in detail the second Rényi entropy of entangled regions at the QCP in the transverse-field Ising model in 2 + 1 space–time dimensions—a fixed point for which there is no exact result for the scaling of entanglement entropy. We calculate a universal coefficient of a vertex-induced logarithmic scaling for a polygonal entangled subregion, and compare the result to interacting and non-interacting theories. We also examine the shape-dependence of the Rényi entropy for finite-size toroidal lattices divided into two entangled cylinders by smooth boundaries. Remarkably, we find that the dependence on cylinder length follows a shape-dependent function calculated previously by Stephan et al (2013 New J. Phys. 15 015004) at the QCP corresponding to the 2 + 1 dimensional quantum Lifshitz free scalar field theory. The quality of the fit of our data to this scaling function, as well as the apparent cutoff-independent coefficient that results, presents tantalizing evidence that this function may reflect universal behaviour across these and other very disparate QCPs in 2 + 1 dimensional systems. (paper)
Final Report: 06-LW-013, Nuclear Physics the Monte Carlo Way
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Ormand, W E
2009-03-01
This is document reports the progress and accomplishments achieved in 2006-2007 with LDRD funding under the proposal 06-LW-013, 'Nuclear Physics the Monte Carlo Way'. The project was a theoretical study to explore a novel approach to dealing with a persistent problem in Monte Carlo approaches to quantum many-body systems. The goal was to implement a solution to the notorious 'sign-problem', which if successful, would permit, for the first time, exact solutions to quantum many-body systems that cannot be addressed with other methods. In this document, we outline the progress and accomplishments achieved during FY2006-2007 with LDRD funding in the proposal 06-LW-013, 'Nuclear Physics the Monte Carlo Way'. This project was funded under the Lab Wide LDRD competition at Lawrence Livermore National Laboratory. The primary objective of this project was to test the feasibility of implementing a novel approach to solving the generic quantum many-body problem, which is one of the most important problems being addressed in theoretical physics today. Instead of traditional methods based matrix diagonalization, this proposal focused a Monte Carlo method. The principal difficulty with Monte Carlo methods, is the so-called 'sign problem'. The sign problem, which will discussed in some detail later, is endemic to Monte Carlo approaches to the quantum many-body problem, and is the principal reason that they have not been completely successful in the past. Here, we outline our research in the 'shifted-contour method' applied the Auxiliary Field Monte Carlo (AFMC) method.
Final Report: 06-LW-013, Nuclear Physics the Monte Carlo Way
International Nuclear Information System (INIS)
This is document reports the progress and accomplishments achieved in 2006-2007 with LDRD funding under the proposal 06-LW-013, 'Nuclear Physics the Monte Carlo Way'. The project was a theoretical study to explore a novel approach to dealing with a persistent problem in Monte Carlo approaches to quantum many-body systems. The goal was to implement a solution to the notorious 'sign-problem', which if successful, would permit, for the first time, exact solutions to quantum many-body systems that cannot be addressed with other methods. In this document, we outline the progress and accomplishments achieved during FY2006-2007 with LDRD funding in the proposal 06-LW-013, 'Nuclear Physics the Monte Carlo Way'. This project was funded under the Lab Wide LDRD competition at Lawrence Livermore National Laboratory. The primary objective of this project was to test the feasibility of implementing a novel approach to solving the generic quantum many-body problem, which is one of the most important problems being addressed in theoretical physics today. Instead of traditional methods based matrix diagonalization, this proposal focused a Monte Carlo method. The principal difficulty with Monte Carlo methods, is the so-called 'sign problem'. The sign problem, which will discussed in some detail later, is endemic to Monte Carlo approaches to the quantum many-body problem, and is the principal reason that they have not been completely successful in the past. Here, we outline our research in the 'shifted-contour method' applied the Auxiliary Field Monte Carlo (AFMC) method
Aneesu-Rahman Prize Lecture: The ``sign problem'' in Quantum Monte Carlo
Ceperley, D. M.
1998-03-01
Quantum simulation methods have been quite successful in giving exact results for certain systems, primarily bosons(Ceperley, D.M. , Rev. Mod. Phys. 67), 279 (1995).. Use of the same techniques in general quantum systems leads to the so-called ``sign problem''; the results are correct but the methods are very inefficient. There are two important questions to ask of a proposed method. Given enough computer time can arbitrarily accurate results be obtained? If so, how long does it take to achieve a given error? There are several methods (released-node or transient estimate) that are exact; the difficulty is in finding a method which also scales well with the number of quantum degrees of freedom. Exact methods, in general, scale exponentially with the number of fermions and in the inverse temperature (or accuracy). At root, the fact that wavefunction is complex or changes sign, gives rise to the poor scaling and the ``sign problem.'' It is not the fermion nature of the system, per se, that causes the difficulty. The desired state is not the absolute ground state. Methods which cancel random walks from positive and negative regions have also been limited to quite small systems because they scale poorly. There are a variety of approximate simulation methods which do scale well, such as variational Monte Carlo, and a variety of fixed-node methods (restricted Path Integral Monte Carlo at non-zero temperature and constrained path methods for lattice models) which fix only boundary conditions not the sampling function. For many systems, the variational and fixed-node methods can be very accurate. The lecture notes and references are on my group's homepage.
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Multideterminant wavefunctions, while having a long history in quantum chemistry, are increasingly being used in highly accurate quantum Monte Carlo calculations. Since the accuracy of QMC is ultimately limited by the quality of the trial wavefunction, multi-Slater determinants wavefunctions offer an attractive alternative to Slater-Jastrow and more sophisticated wavefunction ansatz for several reasons. They can be efficiently calculated, straightforwardly optimized, and systematically improved by increasing the number of included determinants. In spite of their potential, however, the convergence properties of multi-Slater determinant wavefunctions with respect to orbital set choice and excited determinant selection are poorly understood, which hinders the application of these wavefunctions to large systems and solids. In this paper, by performing QMC calculations on the equilibrium and stretched carbon dimer, we find that convergence of the recovered correlation energy with respect to number of determinants can depend quite strongly on basis set and determinant selection methods, especially where there is strong correlation. We demonstrate that properly chosen orbital sets and determinant selection techniques from quantum chemistry methods can dramatically reduce the required number of determinants (and thus the computational cost) to reach a given accuracy, which we argue shows clear need for an automatic QMC-only method for selecting determinants and generating optimal orbital sets
Fracchia, F.; Filippi, C.; Amovilli, C.
2014-01-01
We present here several novel features of our recently proposed Jastrow linear generalized valence bond (J-LGVB) wave functions, which allow a consistently accurate description of complex potential energy surfaces (PES) of medium-large systems within quantum Monte Carlo (QMC). In particular, we deve
Dubecký, Matúš; Jurečka, Petr; Mitas, Lubos; Hobza, Pavel; Otyepka, Michal
2014-01-01
Reliable theoretical predictions of noncovalent interaction energies, which are important e.g. in drug-design and hydrogen-storage applications, belong to longstanding challenges of contemporary quantum chemistry. In this respect, the fixed-node diffusion Monte Carlo (FN-DMC) is a promising alternative to the commonly used ``gold standard'' coupled-cluster CCSD(T)/CBS method for its benchmark accuracy and favourable scaling, in contrast to other correlated wave function approaches. This work is focused on the analysis of protocols and possible tradeoffs for FN-DMC estimations of noncovalent interaction energies and proposes a significantly more efficient yet accurate computational protocol using simplified explicit correlation terms. Its performance is illustrated on a number of weakly bound complexes, including water dimer, benzene/hydrogen, T-shape benzene dimer and stacked adenine-thymine DNA base pair complex. The proposed protocol achieves excellent agreement ($\\sim$0.2 kcal/mol) with respect to the reli...
Semi-stochastic full configuration interaction quantum Monte Carlo: Developments and application
International Nuclear Information System (INIS)
We expand upon the recent semi-stochastic adaptation to full configuration interaction quantum Monte Carlo (FCIQMC). We present an alternate method for generating the deterministic space without a priori knowledge of the wave function and present stochastic efficiencies for a variety of both molecular and lattice systems. The algorithmic details of an efficient semi-stochastic implementation are presented, with particular consideration given to the effect that the adaptation has on parallel performance in FCIQMC. We further demonstrate the benefit for calculation of reduced density matrices in FCIQMC through replica sampling, where the semi-stochastic adaptation seems to have even larger efficiency gains. We then combine these ideas to produce explicitly correlated corrected FCIQMC energies for the beryllium dimer, for which stochastic errors on the order of wavenumber accuracy are achievable
Linear-scaling quantum Monte Carlo technique with non-orthogonal localized orbitals
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We have reformulated the quantum Monte Carlo (QMC) technique so that a large part of the calculation scales linearly with the number of atoms. The reformulation is related to a recent alternative proposal for achieving linear-scaling QMC, based on maximally localized Wannier orbitals (MLWO), but has the advantage of greater simplicity. The technique we propose draws on methods recently developed for linear-scaling density functional theory. We report tests of the new technique on the insulator MgO, and show that its linear-scaling performance is somewhat better than that achieved by the MLWO approach. Implications for the application of QMC to large complex systems are pointed out. (letter to the editor)
Kersten, Jennifer; Alavi, Ali
2016-01-01
The Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method has proved able to provide near-exact solutions to the electronic Schr\\"odinger equation within a finite orbital basis set, without relying on an expansion about a reference state. However, a drawback to the approach is that being based on an expansion of Slater determinants, the FCIQMC method suffers from a basis set incompleteness error that decays very slowly with the size of the employed single particle basis. The FCIQMC results obtained in a small basis set can be improved significantly with explicitly correlated techniques. Here, we present a study that assesses and compares two contrasting `universal' explicitly correlated approaches that fit into the FCIQMC framework; the $[2]_{R12}$ method of Valeev {\\em et al.}, and the explicitly correlated canonical transcorrelation approach of Yanai {\\em et al}. The former is an {\\em a posteriori} internally-contracted perturbative approach, while the latter transforms the Hamiltonian prior to...
Ground-state properties of LiH by reptation quantum Monte Carlo methods.
Ospadov, Egor; Oblinsky, Daniel G; Rothstein, Stuart M
2011-05-01
We apply reptation quantum Monte Carlo to calculate one- and two-electron properties for ground-state LiH, including all tensor components for static polarizabilities and hyperpolarizabilities to fourth-order in the field. The importance sampling is performed with a large (QZ4P) STO basis set single determinant, directly obtained from commercial software, without incurring the overhead of optimizing many-parameter Jastrow-type functions of the inter-electronic and internuclear distances. We present formulas for the electrical response properties free from the finite-field approximation, which can be problematic for the purposes of stochastic estimation. The α, γ, A and C polarizability values are reasonably consistent with recent determinations reported in the literature, where they exist. A sum rule is obeyed for components of the B tensor, but B(zz,zz) as well as β(zzz) differ from what was reported in the literature. PMID:21445452
Boosting the accuracy and speed of quantum Monte Carlo: size-consistency and time-step
Zen, Andrea; Gillan, Michael J; Michaelides, Angelos; Alfè, Dario
2016-01-01
Diffusion Monte Carlo (DMC) simulations for fermions are becoming the standard to provide high quality reference data in systems that are too large to be investigated via quantum chemical approaches. DMC with the fixed-node approximation relies on modifications of the Green function to avoid singularities near the nodal surface of the trial wavefunction. We show that these modifications affect the DMC energies in a way that is not size-consistent, resulting in large time-step errors. Building on the modifications of Umrigar {\\em et al.} and of DePasquale {\\em et al.} we propose a simple Green function modification that restores size-consistency to large values of time-step; substantially reducing the time-step errors. The new algorithm also yields remarkable speedups of up to two orders of magnitude in the calculation of molecule-molecule binding energies and crystal cohesive energies, thus extending the horizons of what is possible with DMC.
Phase Stability of TiO$_2$ Polymorphs from Diffusion Quantum Monte Carlo
Luo, Ye; Shulenburger, Luke; Krogel, Jaron T; Heinonen, Olle; Kent, Paul R C
2016-01-01
Titanium dioxide, TiO$_2$, has multiple applications in catalysis, energy conversion and memristive devices because of its electronic structure. Most of these applications utilize the naturally existing phases: rutile, anatase and brookite. Despite the simple form of TiO$_2$ and its wide uses, there is long-standing disagreement between theory and experiment on the energetic ordering of these phases that has never been resolved. We present the first analysis of phase stability at zero temperature using the highly accurate many-body fixed node diffusion Quantum Monte Carlo (QMC) method. We also include the effects of temperature by calculating the Helmholtz free energy including both internal energy and vibrational contributions from density functional perturbation theory based quasi harmonic phonon calculations. Our QMC calculations find that anatase is the most stable phase at zero temperature, consistent with many previous mean-field calculations. However, at elevated temperatures, rutile becomes the most s...
Simple formalism for efficient derivatives and multi-determinant expansions in quantum Monte Carlo
Filippi, Claudia; Assaraf, Roland; Moroni, Saverio
2016-05-01
We present a simple and general formalism to compute efficiently the derivatives of a multi-determinant Jastrow-Slater wave function, the local energy, the interatomic forces, and similar quantities needed in quantum Monte Carlo. Through a straightforward manipulation of matrices evaluated on the occupied and virtual orbitals, we obtain an efficiency equivalent to algorithmic differentiation in the computation of the interatomic forces and the optimization of the orbital parameters. Furthermore, for a large multi-determinant expansion, the significant computational gain afforded by a recently introduced table method is here extended to the local value of any one-body operator and to its derivatives, in both all-electron and pseudopotential calculations.
Linear-scaling evaluation of the local energy in quantum MonteCarlo
Energy Technology Data Exchange (ETDEWEB)
Austin, Brian; Aspuru-Guzik, Alan; Salomon-Ferrer, Romelia; Lester Jr., William A.
2006-02-11
For atomic and molecular quantum Monte Carlo calculations, most of the computational effort is spent in the evaluation of the local energy. We describe a scheme for reducing the computational cost of the evaluation of the Slater determinants and correlation function for the correlated molecular orbital (CMO) ansatz. A sparse representation of the Slater determinants makes possible efficient evaluation of molecular orbitals. A modification to the scaled distance function facilitates a linear scaling implementation of the Schmidt-Moskowitz-Boys-Handy (SMBH) correlation function that preserves the efficient matrix multiplication structure of the SMBH function. For the evaluation of the local energy, these two methods lead to asymptotic linear scaling with respect to the molecule size.
Linear-scaling evaluation of the local energy in quantum Monte Carlo
International Nuclear Information System (INIS)
For atomic and molecular quantum Monte Carlo calculations, most of the computational effort is spent in the evaluation of the local energy. We describe a scheme for reducing the computational cost of the evaluation of the Slater determinants and correlation function for the correlated molecular orbital (CMO) ansatz. A sparse representation of the Slater determinants makes possible efficient evaluation of molecular orbitals. A modification to the scaled distance function facilitates a linear scaling implementation of the Schmidt-Moskowitz-Boys-Handy (SMBH) correlation function that preserves the efficient matrix multiplication structure of the SMBH function. For the evaluation of the local energy, these two methods lead to asymptotic linear scaling with respect to the molecule size
Thomas, Robert E; Overy, Catherine; Knowles, Peter J; Alavi, Ali; Booth, George H
2015-01-01
Unbiased stochastic sampling of the one- and two-body reduced density matrices is achieved in full configuration interaction quantum Monte Carlo with the introduction of a second, "replica" ensemble of walkers, whose population evolves in imaginary time independently from the first, and which entails only modest additional computational overheads. The matrices obtained from this approach are shown to be representative of full configuration-interaction quality, and hence provide a realistic opportunity to achieve high-quality results for a range of properties whose operators do not necessarily commute with the hamiltonian. A density-matrix formulated quasi-variational energy estimator having been already proposed and investigated, the present work extends the scope of the theory to take in studies of analytic nuclear forces, molecular dipole moments and polarisabilities, with extensive comparison to exact results where possible. These new results confirm the suitability of the sampling technique and, where suf...
Energy Technology Data Exchange (ETDEWEB)
Clay, Raymond C. [Univ. of Illinois, Urbana, IL (United States); Mcminis, Jeremy [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); McMahon, Jeffrey M. [Univ. of Illinois, Urbana, IL (United States); Pierleoni, Carlo [Istituto Nazionale di Fisica Nucleare (INFN), L' aquila (Italy). Lab. Nazionali del Gran Sasso (INFN-LNGS); Ceperley, David M. [Univ. of Illinois, Urbana, IL (United States); Morales, Miguel A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2014-05-01
The ab initio phase diagram of dense hydrogen is very sensitive to errors in the treatment of electronic correlation. Recently, it has been shown that the choice of the density functional has a large effect on the predicted location of both the liquid-liquid phase transition and the solid insulator-to-metal transition in dense hydrogen. To identify the most accurate functional for dense hydrogen applications, we systematically benchmark some of the most commonly used functionals using quantum Monte Carlo. By considering several measures of functional accuracy, we conclude that the van der Waals and hybrid functionals significantly outperform local density approximation and Perdew-Burke-Ernzerhof. We support these conclusions by analyzing the impact of functional choice on structural optimization in the molecular solid, and on the location of the liquid-liquid phase transition.
A Quantum Monte Carlo Study of mono(benzene)TM and bis(benzene)TM Systems
Bennett, M Chandler; Mitas, Lubos
2016-01-01
We present a study of mono(benzene)TM and bis(benzene)TM systems, where TM={Mo,W}. We calculate the binding energies by quantum Monte Carlo (QMC) approaches and compare the results with other methods and available experiments. The orbitals for the determinantal part of each trial wave function were generated from several types of DFT in order to optimize for fixed-node errors. We estimate and compare the size of the fixed-node errors for both the Mo and W systems with regard to the electron density and degree of localization in these systems. For the W systems we provide benchmarking results of the binding energies, given that experimental data is not available.
Resonating Valence Bond Quantum Monte Carlo: Application to the ozone molecule
Azadi, Sam; Kühne, Thomas D
2015-01-01
We study the potential energy surface of the ozone molecule by means of Quantum Monte Carlo simulations based on the resonating valence bond concept. The trial wave function consists of an antisymmetrized geminal power arranged in a single-determinant that is multiplied by a Jastrow correlation factor. Whereas the determinantal part incorporates static correlation effects, the augmented real-space correlation factor accounts for the dynamics electron correlation. The accuracy of this approach is demonstrated by computing the potential energy surface for the ozone molecule in three vibrational states: symmetric, asymmetric and scissoring. We find that the employed wave function provides a detailed description of rather strongly-correlated multi-reference systems, which is in quantitative agreement with experiment.
Quantum Monte Carlo simulations of strongly coupled quark-gluon plasma
International Nuclear Information System (INIS)
Complete text of publication follows. In recent years, there has been an increasing interest in dynamics and thermodynamics of non-Abelian plasmas at both very high temperature and density. It is expected that a specific state of matter with unconfined quarks and gluons - the so called quark - gluon plasma (QGP) - can exist. The most fundamental way to compute properties of the strongly interacting matter is provided by the lattice QCD. Interpretation of these very complicated computations requires application of various QCD motivated, albeit schematic, models simulating various aspects of the full theory. Moreover, such models are needed in cases when the lattice QCD fails, e.g. at large baryon chemical potentials and out of equilibrium. A semi-classical approximation, based on a point like quasi-particle picture has been recently introduced in literature. It is expected that it allows to treat soft processes in the QGP which are not accessible by the perturbative means and the main features of non-Abelian plasmas can be understood in simple semi-classical terms without the difficulties inherent to a full quantum field theoretical analysis. Here we propose stochastic simulation of thermodynamics and kinetic properties for QGP in semiclassical approximation in the wide region of temperature, density and quasi-particles masses. We extend previous classical nonrelativistic simulations based on a color Coulomb interaction to the quantum regime and take into account the Fermi (Bose) statistics of quarks (gluons) and quantum degeneracy self-consistently. In grand canonical ensemble for finite and zero baryon chemical potential we use the direct quantum path integral Monte Carlo method (PIMC) developed for finite temperature within Feynman formulation of quantum mechanics to do calculations of internal energy, pressure and pair correlation functions. The QGP quasi-particles representing dressed quarks, antiquarks and gluons interact via color quantum Kelbg
Deterministic flows of order-parameters in stochastic processes of quantum Monte Carlo method
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In terms of the stochastic process of quantum-mechanical version of Markov chain Monte Carlo method (the MCMC), we analytically derive macroscopically deterministic flow equations of order parameters such as spontaneous magnetization in infinite-range (d(= ∞)-dimensional) quantum spin systems. By means of the Trotter decomposition, we consider the transition probability of Glauber-type dynamics of microscopic states for the corresponding (d + 1)-dimensional classical system. Under the static approximation, differential equations with respect to macroscopic order parameters are explicitly obtained from the master equation that describes the microscopic-law. In the steady state, we show that the equations are identical to the saddle point equations for the equilibrium state of the same system. The equation for the dynamical Ising model is recovered in the classical limit. We also check the validity of the static approximation by making use of computer simulations for finite size systems and discuss several possible extensions of our approach to disordered spin systems for statistical-mechanical informatics. Especially, we shall use our procedure to evaluate the decoding process of Bayesian image restoration. With the assistance of the concept of dynamical replica theory (the DRT), we derive the zero-temperature flow equation of image restoration measure showing some 'non-monotonic' behaviour in its time evolution.
Monte carlo simulation study of the square lattice S=1/2 quantum heisenberg antiferromagnet
Kim, J K
1999-01-01
For the two dimensional S= 1/2 isotopic quantum Heisenberg antiferromagnet on a square lattice, we report our results of an extensive quantum Monte Carlo simulation for various physical observables such as the correlation length xi, the staggered magnetic susceptibility chi sub S sub T , the structure factor peak value S(Q), the internal energy epsilon, and the uniform susceptibility chi sub u. We find that chi sub S sub T approx chi sup 2 T and S(Q) approx xi sup 2 T sup 2 , in agreement with the predictions of the conventional theory but in disagreement with recent experiments. Our estimate of the spin stiffness constant rho sub s and spin wave velocity c, from the low temperature behavior of the chi sub u is shown to be consistent with the theoretical prediction of the low temperature behavior of the epsilon, and of the xi provided an additional correction up to T sup 2. However, our data are definitely inconsistent with the scenario of the crossover for the xi.
Querlioz, Damien
2013-01-01
This book gives an overview of the quantum transport approaches for nanodevices and focuses on the Wigner formalism. It details the implementation of a particle-based Monte Carlo solution of the Wigner transport equation and how the technique is applied to typical devices exhibiting quantum phenomena, such as the resonant tunnelling diode, the ultra-short silicon MOSFET and the carbon nanotube transistor. In the final part, decoherence theory is used to explain the emergence of the semi-classical transport in nanodevices.
Boxberg, Fredrik; Tulkki, Jukka; Yusa, Go; Sakaki, Hiroyuki
2006-01-01
We have developed a theoretical model to analyze the anomalous cooling of radiative quantum dot (QD) excitons by THz radiation reported by Yusa et al [Proc. 24th ICPS, 1083 (1998)]. We have made three-dimensional (3D) modeling of the strain and the piezoelectric field and calculated the 3D density of states of strain induced quantum dots. On the basis of this analysis we have developed a spin dependent Monte Carlo model, which describes the carrier dynamics in QD's when the intraband relaxati...
Patrascu, Andrei T
2014-01-01
I present here a new method that allows the introduction of a discrete auxiliary symmetry in a theory in such a way that the eigenvalue spectrum of the fermion functional determinant is made up of complex conjugated pairs. The method implies a particular way of introducing and integrating over auxiliary fields related to a set of artificial shift symmetries. Gauge-fixing the artificial continuous shift symmetries in the direct and dual sector leads to the implementation of a Kahler structure over the field space. The discrete symmetry appears to be induced by the Hodge-* operator. The particular extension of the field space presented here makes the operators of the de-Rham cohomology manifest. This method implies the identification of the (anti)-BRST and dual-(anti)-BRST operators with the exterior derivative and its dual in the context of the complex de-Rham cohomology. The novelty of this method relies on the fact that the field structure is doubled two times in order to make use of a supplemental symmetry ...
Saito, Hiroki
2016-05-01
Motivated by recent experiments [H. Kadau et al., Nature (London) 530, 194 (2016); I. Ferrier-Barbut et al., arXiv:1601.03318] and theoretical prediction (F. Wächtler and L. Santos, arXiv:1601.04501), the ground state of a dysprosium Bose-Einstein condensate with strong dipole-dipole interaction is studied by the path-integral Monte Carlo method. It is shown that quantum fluctuation can stabilize the condensate against dipolar collapse.
Pavlovsky, Oleg
2011-01-01
We propose a new Monte-Carlo method for calculation of the Casimir forces. Our method is based on the formalism of noncompact lattice quantum electrodynamics. This approach has been tested in the simplest case of two ideal conducting planes. After this the method has been applied to the calculation of the lateral Casimir forces between two ideal conducting rectangular gratings. We compare our calculations with the results of PFA and "Optimal" PFA methods.
International Nuclear Information System (INIS)
Unbiased stochastic sampling of the one- and two-body reduced density matrices is achieved in full configuration interaction quantum Monte Carlo with the introduction of a second, “replica” ensemble of walkers, whose population evolves in imaginary time independently from the first and which entails only modest additional computational overheads. The matrices obtained from this approach are shown to be representative of full configuration-interaction quality and hence provide a realistic opportunity to achieve high-quality results for a range of properties whose operators do not necessarily commute with the Hamiltonian. A density-matrix formulated quasi-variational energy estimator having been already proposed and investigated, the present work extends the scope of the theory to take in studies of analytic nuclear forces, molecular dipole moments, and polarisabilities, with extensive comparison to exact results where possible. These new results confirm the suitability of the sampling technique and, where sufficiently large basis sets are available, achieve close agreement with experimental values, expanding the scope of the method to new areas of investigation
Kersten, J. A. F.; Booth, George H.; Alavi, Ali
2016-08-01
The Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method has proved able to provide near-exact solutions to the electronic Schrödinger equation within a finite orbital basis set, without relying on an expansion about a reference state. However, a drawback to the approach is that being based on an expansion of Slater determinants, the FCIQMC method suffers from a basis set incompleteness error that decays very slowly with the size of the employed single particle basis. The FCIQMC results obtained in a small basis set can be improved significantly with explicitly correlated techniques. Here, we present a study that assesses and compares two contrasting "universal" explicitly correlated approaches that fit into the FCIQMC framework: the [2]R12 method of Kong and Valeev [J. Chem. Phys. 135, 214105 (2011)] and the explicitly correlated canonical transcorrelation approach of Yanai and Shiozaki [J. Chem. Phys. 136, 084107 (2012)]. The former is an a posteriori internally contracted perturbative approach, while the latter transforms the Hamiltonian prior to the FCIQMC simulation. These comparisons are made across the 55 molecules of the G1 standard set. We found that both methods consistently reduce the basis set incompleteness, for accurate atomization energies in small basis sets, reducing the error from 28 mEh to 3-4 mEh. While many of the conclusions hold in general for any combination of multireference approaches with these methodologies, we also consider FCIQMC-specific advantages of each approach.
International Nuclear Information System (INIS)
Various strategies to implement efficiently quantum Monte Carlo (QMC) simulations for large chemical systems are presented. These include: (i) the introduction of an efficient algorithm to calculate the computationally expensive Slater matrices. This novel scheme is based on the use of the highly localized character of atomic Gaussian basis functions (not the molecular orbitals as usually done), (ii) the possibility of keeping the memory footprint minimal, (iii) the important enhancement of single-core performance when efficient optimization tools are used, and (iv) the definition of a universal, dynamic, fault-tolerant, and load-balanced framework adapted to all kinds of computational platforms (massively parallel machines, clusters, or distributed grids). These strategies have been implemented in the QMC-Chem code developed at Toulouse and illustrated with numerical applications on small peptides of increasing sizes (158, 434, 1056, and 1731 electrons). Using 10-80 k computing cores of the Curie machine (GENCI-TGCC-CEA, France), QMC-Chem has been shown to be capable of running at the peta scale level, thus demonstrating that for this machine a large part of the peak performance can be achieved. Implementation of large-scale QMC simulations for future exa scale platforms with a comparable level of efficiency is expected to be feasible. (authors)
Comparison of polynomial approximations to speed up planewave-based quantum Monte Carlo calculations
Parker, William D; Alfè, Dario; Hennig, Richard G; Wilkins, John W
2013-01-01
The computational cost of quantum Monte Carlo (QMC) calculations of realistic periodic systems depends strongly on the method of storing and evaluating the many-particle wave function. Previous work [A. J. Williamson et al., Phys. Rev. Lett. 87, 246406 (2001); D. Alf\\`e and M. J. Gillan, Phys. Rev. B 70, 161101 (2004)] has demonstrated the reduction of the O(N^3) cost of evaluating the Slater determinant with planewaves to O(N^2) using localized basis functions. We compare four polynomial approximations as basis functions -- interpolating Lagrange polynomials, interpolating piecewise-polynomial-form (pp-) splines, and basis-form (B-) splines (interpolating and smoothing). All these basis functions provide a similar speedup relative to the planewave basis. The pp-splines have eight times the memory requirement of the other methods. To test the accuracy of the basis functions, we apply them to the ground state structures of Si, Al, and MgO. The polynomial approximations differ in accuracy most strongly for MgO ...
Quantum monte carlo study of the energetics of small hydrogenated and fluoride lithium clusters.
Moreira, N L; Brito, B G A; Rabelo, J N Teixeira; Cândido, Ladir
2016-06-30
An investigation of the energetics of small lithium clusters doped either with a hydrogen or with a fluorine atom as a function of the number of lithium atoms using fixed-node diffusion quantum Monte Carlo (DMC) simulation is reported. It is found that the binding energy (BE) for the doped clusters increases in absolute values leading to a more stable system than for the pure ones in excellent agreement with available experimental measurements. The BE increases for pure, remains almost constant for hydrogenated, and decreases rapidly toward the bulk lithium for the fluoride as a function of the number of lithium atoms in the clusters. The BE, dissociation energy as well as the second difference in energy display a pronounced odd-even oscillation with the number of lithium atoms. The electron correlation inverts the odd-even oscillation pattern for the doped in comparison with the pure clusters and has an impact of 29%-83% to the BE being higher in the pure cluster followed by the hydrogenated and then by the fluoride. The dissociation energy and the second difference in energy indicate that the doped cluster Li3 H is the most stable whereas among the pure ones the more stable are Li2 , Li4 , and Li6 . The electron correlation energy is crucial for the stabilization of Li3 H. © 2016 Wiley Periodicals, Inc. PMID:26992447
Clay, Raymond C.; Holzmann, Markus; Ceperley, David M.; Morales, Miguel A.
2016-01-01
An accurate understanding of the phase diagram of dense hydrogen and helium mixtures is a crucial component in the construction of accurate models of Jupiter, Saturn, and Jovian extrasolar planets. Though density-functional-theory-based first-principles methods have the potential to provide the accuracy and computational efficiency required for this task, recent benchmarking in hydrogen has shown that achieving this accuracy requires a judicious choice of functional, and a quantification of the errors introduced. In this work, we present a quantum Monte Carlo (QMC) -based benchmarking study of a wide range of density functionals for use in hydrogen-helium mixtures at thermodynamic conditions relevant for Jovian planets. Not only do we continue our program of benchmarking energetics and pressures, but we deploy QMC-based force estimators and use them to gain insight into how well the local liquid structure is captured by different density functionals. We find that TPSS, BLYP, and vdW-DF are the most accurate functionals by most metrics, and that the enthalpy, energy, and pressure errors are very well behaved as a function of helium concentration. Beyond this, we highlight and analyze the major error trends and relative differences exhibited by the major classes of functionals, and we estimate the magnitudes of these effects when possible.
Hanada, Masanori; Miwa, Akitsugu; Nishimura, Jun; Takeuchi, Shingo
2009-05-01
In the string-gauge duality it is important to understand how the space-time geometry is encoded in gauge theory observables. We address this issue in the case of the D0-brane system at finite temperature T. Based on the duality, the temporal Wilson loop W in gauge theory is expected to contain the information of the Schwarzschild radius RSch of the dual black hole geometry as log(W)=RSch/(2pialpha'T). This translates to the power-law behavior log(W)=1.89(T/lambda 1/3)-3/5, where lambda is the 't Hooft coupling constant. We calculate the Wilson loop on the gauge theory side in the strongly coupled regime by performing Monte Carlo simulations of supersymmetric matrix quantum mechanics with 16 supercharges. The results reproduce the expected power-law behavior up to a constant shift, which is explainable as alpha' corrections on the gravity side. Our conclusion also demonstrates manifestly the fuzzball picture of black holes. PMID:19518857
Kersten, J A F; Booth, George H; Alavi, Ali
2016-08-01
The Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method has proved able to provide near-exact solutions to the electronic Schrödinger equation within a finite orbital basis set, without relying on an expansion about a reference state. However, a drawback to the approach is that being based on an expansion of Slater determinants, the FCIQMC method suffers from a basis set incompleteness error that decays very slowly with the size of the employed single particle basis. The FCIQMC results obtained in a small basis set can be improved significantly with explicitly correlated techniques. Here, we present a study that assesses and compares two contrasting "universal" explicitly correlated approaches that fit into the FCIQMC framework: the [2]R12 method of Kong and Valeev [J. Chem. Phys. 135, 214105 (2011)] and the explicitly correlated canonical transcorrelation approach of Yanai and Shiozaki [J. Chem. Phys. 136, 084107 (2012)]. The former is an a posteriori internally contracted perturbative approach, while the latter transforms the Hamiltonian prior to the FCIQMC simulation. These comparisons are made across the 55 molecules of the G1 standard set. We found that both methods consistently reduce the basis set incompleteness, for accurate atomization energies in small basis sets, reducing the error from 28 mEh to 3-4 mEh. While many of the conclusions hold in general for any combination of multireference approaches with these methodologies, we also consider FCIQMC-specific advantages of each approach. PMID:27497549
Multigrid Hirsch-Fye quantum Monte Carlo solver for dynamical mean-field theory
International Nuclear Information System (INIS)
The dynamical mean-field theory (DMFT) is a nonperturbative approach to Hubbard-type models in which an impurity model has to be solved self-consistently. This is possible nonperturbatively using the Hirsch-Fye quantum Monte-Carlo (HF-QMC) algorithm which introduces an imaginary-time discretization Δτ. The associated Trotter error impacts all ''raw'' HF-QMC results including phase boundaries, Green functions, spectra, and scalar observables such as energies and quasiparticle weights. Unbiased estimates of scalar observables can be derived from HF-QMC data by extrapolation Δτ→ 0, with high precision and efficiency. However, this a posteriori correction of the Trotter error is problematic close to phase boundaries and could so far not be applied to Green functions and spectra. In this talk, I show how numerically exact Green functions can be extrapolated from HF-QMC estimates and construct a multigrid HF-QMC algorithm which eliminates the discretization error within the DMFT self-consistency cycle. In contrast to conventional HF-QMC, the multigrid algorithm converges to the numerically exact fixed point(s) and allows for the direct determination of phase boundaries without further extrapolation. It extends the useful range of Δτ values and yields unbiased estimates of observables with high precision and efficiency, even close to phase transitions
Quantum Monte Carlo simulation study of two-dimensional Hubbard model
International Nuclear Information System (INIS)
The physical properties of strongly correlated fermionic systems, described by two-dimensional Hubbard model with nearest neighbour hopping have been studied using the path integral formulation along with quantum Monte Carlo simulation technique. The partition function of the fermionic system is evaluated within the usual path integral formulation, treating β, the inverse temperature as imaginary time and dividing it into small discrete intervals. The singlet and triplet pairing correlation functions, nearest-neighbour charge density correlations, local squared magnetic moments, double occupancy and total energy are studied as a function of interaction strength for various band fillings at different temperatures. This study leads to the conclusions that the singlet pairing correlation decreases with increasing interaction strength. The triplet pairing correlations for parallel spins show abrupt behaviour. The extended singlet pairing correlation and triplet pairing correlations for anti-parallel spins show the slightly fluctuating behaviour of finite temperatures. The enhancement of local squared magnetic moment and decrement of double occupancy and increment of total energy with U at finite temperatures for half-filled, one-third-filled and one-fourth-filled bands are also noted. (author)
Energy Technology Data Exchange (ETDEWEB)
Zhuang Guilin, E-mail: glzhuang@zjut.edu.cn [Institute of Industrial Catalysis, College of Chemical Engineering and Materials Science, Zhejiang University of Technology, Hangzhou 310032 (China); Chen Wulin [Institute of Industrial Catalysis, College of Chemical Engineering and Materials Science, Zhejiang University of Technology, Hangzhou 310032 (China); Zheng Jun [Center of Modern Experimental Technology, Anhui University, Hefei 230039 (China); Yu Huiyou [Institute of Industrial Catalysis, College of Chemical Engineering and Materials Science, Zhejiang University of Technology, Hangzhou 310032 (China); Wang Jianguo, E-mail: jgw@zjut.edu.cn [Institute of Industrial Catalysis, College of Chemical Engineering and Materials Science, Zhejiang University of Technology, Hangzhou 310032 (China)
2012-08-15
A series of lanthanide coordination polymers have been obtained through the hydrothermal reaction of N-(sulfoethyl) iminodiacetic acid (H{sub 3}SIDA) and Ln(NO{sub 3}){sub 3} (Ln=La, 1; Pr, 2; Nd, 3; Gd, 4). Crystal structure analysis exhibits that lanthanide ions affect the coordination number, bond length and dimension of compounds 1-4, which reveal that their structure diversity can be attributed to the effect of lanthanide contraction. Furthermore, the combination of magnetic measure with quantum Monte Carlo(QMC) studies exhibits that the coupling parameters between two adjacent Gd{sup 3+} ions for anti-anti and syn-anti carboxylate bridges are -1.0 Multiplication-Sign 10{sup -3} and -5.0 Multiplication-Sign 10{sup -3} cm{sup -1}, respectively, which reveals weak antiferromagnetic interaction in 4. - Graphical abstract: Four lanthanide coordination polymers with N-(sulfoethyl) iminodiacetic acid were obtained under hydrothermal condition and reveal the weak antiferromagnetic coupling between two Gd{sup 3+} ions by Quantum Monte Carlo studies. Highlights: Black-Right-Pointing-Pointer Four lanthanide coordination polymers of H{sub 3}SIDA ligand were obtained. Black-Right-Pointing-Pointer Lanthanide ions play an important role in their structural diversity. Black-Right-Pointing-Pointer Magnetic measure exhibits that compound 4 features antiferromagnetic property. Black-Right-Pointing-Pointer Quantum Monte Carlo studies reveal the coupling parameters of two Gd{sup 3+} ions.
Directory of Open Access Journals (Sweden)
Wagner Fernando Delfino Angelotti
2008-01-01
Full Text Available The paper presents an introductory and general discussion on the quantum Monte Carlo methods, some fundamental algorithms, concepts and applicability. In order to introduce the quantum Monte Carlo method, preliminary concepts associated with Monte Carlo techniques are discussed.
Multiple-Resonance Local Wave Functions for Accurate Excited States in Quantum Monte Carlo.
Zulfikri, Habiburrahman; Amovilli, Claudio; Filippi, Claudia
2016-03-01
We introduce a novel class of local multideterminant Jastrow-Slater wave functions for the efficient and accurate treatment of excited states in quantum Monte Carlo. The wave function is expanded as a linear combination of excitations built from multiple sets of localized orbitals that correspond to the bonding patterns of the different Lewis resonance structures of the molecule. We capitalize on the concept of orbital domains of local coupled-cluster methods, which is here applied to the active space to select the orbitals to correlate and construct the important transitions. The excitations are further grouped into classes, which are ordered in importance and can be systematically included in the Jastrow-Slater wave function to ensure a balanced description of all states of interest. We assess the performance of the proposed wave function in the calculation of vertical excitation energies and excited-state geometry optimization of retinal models whose π → π* state has a strong intramolecular charge-transfer character. We find that our multiresonance wave functions recover the reference values of the total energies of the ground and excited states with only a small number of excitations and that the same expansion can be flexibly used at very different geometries. Furthermore, significant computational saving can also be gained in the orbital optimization step by selectively mixing occupied and virtual orbitals based on spatial considerations without loss of accuracy on the excitation energy. Our multiresonance wave functions are therefore compact, accurate, and very promising for the calculation of multiple excited states of different character in large molecules. PMID:26761421
A constrained-path quantum Monte-Carlo approach for the nuclear shell model
International Nuclear Information System (INIS)
The shell model is a powerful theoretical framework for studying the nuclear structure. Unfortunately, the exponential scaling of the many-body space with the number of nucleons or the number of valence levels strongly restricts its applicability. The Quantum Monte-Carlo (QMC) methods may then be considered as a possible alternative to the direct diagonalization of the Hamiltonian. They are based on a stochastic reformulation of the Schroedinger equation to reduce the many-body problem to a set of one-body problems, numerically tractable, describing independent particles that evolve in fluctuating external fields. The originality of the QMC scheme proposed in the present thesis is the use of a variational approach, with symmetry restoration before variation, to guide the Brownian motion and to constrain it in order to control the sign/phase problem that generally occurs in the QMC samplings for fermions. The 'yrast' spectroscopy we obtain for sd- and fp-shell nuclei with realistic residual interactions agree remarkably well with the results from an exact diagonalization of the Hamiltonian. Moreover, an openness towards strongly correlated electronic systems is presented through new QMC schemes recently developed for the two-dimensional Hubbard model. In contrast with the traditional samplings, they guarantee positive-weighted trajectories regardless the on-site interaction strength or the doping of the lattice. We demonstrate that these schemes are in fact related to the stochastic approach applied to the nuclear shell model. The origin of the systematic errors that emerge in these methods, although free from sign/phase problem with the Hubbard Hamiltonian, is also discussed. (author)
Electronic excitations in a dielectric continuum solvent with quantum Monte Carlo: Acrolein in water
International Nuclear Information System (INIS)
We investigate here the vertical n → π* and π → π* transitions of s-trans-acrolein in aqueous solution by means of a polarizable continuum model (PCM) we have developed for the treatment of the solute at the quantum Monte Carlo (QMC) level of the theory. We employ the QMC approach which allows us to work with highly correlated electronic wave functions for both the solute ground and excited states and, to study the vertical transitions in the solvent, adopt the commonly used scheme of considering fast and slow dielectric polarization. To perform calculations in a non-equilibrium solvation regime for the solute excited state, we add a correction to the global dielectric polarization charge density, obtained self consistently with the solute ground-state wave function by assuming a linear-response scheme. For the solvent polarization in the field of the solute in the ground state, we use the static dielectric constant while, for the electronic dielectric polarization, we employ the solvent refractive index evaluated at the same frequency of the photon absorbed by the solute for the transition. This choice is shown to be better than adopting the most commonly used value of refractive index measured in the region of visible radiation. Our QMC calculations show that, for standard cavities, the solvatochromic shifts obtained with the PCM are underestimated, even though of the correct sign, for both transitions of acrolein in water. Only by reducing the size of the cavity to values where more than one electron is escaped to the solvent region, we regain the experimental shift for the n → π* case and also improve considerably the shift for the π → π* transition
Electronic excitations in a dielectric continuum solvent with quantum Monte Carlo: Acrolein in water
Floris, Franca Maria; Filippi, Claudia; Amovilli, Claudio
2014-01-01
We investigate here the vertical n → π* and π → π* transitions of s-trans-acrolein in aqueous solution by means of a polarizable continuum model (PCM) we have developed for the treatment of the solute at the quantum Monte Carlo (QMC) level of the theory. We employ the QMC approach which allows us to work with highly correlated electronic wave functions for both the solute ground and excited states and, to study the vertical transitions in the solvent, adopt the commonly used scheme of considering fast and slow dielectric polarization. To perform calculations in a non-equilibrium solvation regime for the solute excited state, we add a correction to the global dielectric polarization charge density, obtained self consistently with the solute ground-state wave function by assuming a linear-response scheme. For the solvent polarization in the field of the solute in the ground state, we use the static dielectric constant while, for the electronic dielectric polarization, we employ the solvent refractive index evaluated at the same frequency of the photon absorbed by the solute for the transition. This choice is shown to be better than adopting the most commonly used value of refractive index measured in the region of visible radiation. Our QMC calculations show that, for standard cavities, the solvatochromic shifts obtained with the PCM are underestimated, even though of the correct sign, for both transitions of acrolein in water. Only by reducing the size of the cavity to values where more than one electron is escaped to the solvent region, we regain the experimental shift for the n → π* case and also improve considerably the shift for the π → π* transition.
Electronic excitations in a dielectric continuum solvent with quantum Monte Carlo: Acrolein in water
Energy Technology Data Exchange (ETDEWEB)
Floris, Franca Maria, E-mail: floris@dcci.unipi.it; Amovilli, Claudio [Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via Risorgimento 35, 56126 Pisa (Italy); Filippi, Claudia [MESA Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands)
2014-01-21
We investigate here the vertical n → π{sup *} and π → π{sup *} transitions of s-trans-acrolein in aqueous solution by means of a polarizable continuum model (PCM) we have developed for the treatment of the solute at the quantum Monte Carlo (QMC) level of the theory. We employ the QMC approach which allows us to work with highly correlated electronic wave functions for both the solute ground and excited states and, to study the vertical transitions in the solvent, adopt the commonly used scheme of considering fast and slow dielectric polarization. To perform calculations in a non-equilibrium solvation regime for the solute excited state, we add a correction to the global dielectric polarization charge density, obtained self consistently with the solute ground-state wave function by assuming a linear-response scheme. For the solvent polarization in the field of the solute in the ground state, we use the static dielectric constant while, for the electronic dielectric polarization, we employ the solvent refractive index evaluated at the same frequency of the photon absorbed by the solute for the transition. This choice is shown to be better than adopting the most commonly used value of refractive index measured in the region of visible radiation. Our QMC calculations show that, for standard cavities, the solvatochromic shifts obtained with the PCM are underestimated, even though of the correct sign, for both transitions of acrolein in water. Only by reducing the size of the cavity to values where more than one electron is escaped to the solvent region, we regain the experimental shift for the n → π{sup *} case and also improve considerably the shift for the π → π{sup *} transition.
Directory of Open Access Journals (Sweden)
Claudio Amovilli
2016-02-01
Full Text Available In this work, we present a simple decomposition scheme of the Kohn-Sham optimized orbitals which is able to provide a reduced basis set, made of localized polycentric orbitals, specifically designed for Quantum Monte Carlo. The decomposition follows a standard Density functional theory (DFT calculation and is based on atomic connectivity and shell structure. The new orbitals are used to construct a compact correlated wave function of the Slater–Jastrow form which is optimized at the Variational Monte Carlo level and then used as the trial wave function for a final Diffusion Monte Carlo accurate energy calculation. We are able, in this way, to capture the basic information on the real system brought by the Kohn-Sham orbitals and use it for the calculation of the ground state energy within a strictly variational method. Here, we show test calculations performed on some small selected systems to assess the validity of the proposed approach in a molecular fragmentation, in the calculation of a barrier height of a chemical reaction and in the determination of intermolecular potentials. The final Diffusion Monte Carlo energies are in very good agreement with the best literature data within chemical accuracy.
Brito, B. G. A.; Cândido, Ladir; Hai, G.-Q.; Peeters, F. M.
2015-11-01
In order to study quantum effects in a two-dimensional crystal lattice of a free-standing monolayer graphene, we have performed both path-integral Monte Carlo (PIMC) and classical Monte Carlo (MC) simulations for temperatures up to 2000 K. The REBO potential is used for the interatomic interaction. The total energy, interatomic distance, root-mean-square displacement of the atom vibrations, and the free energy of the graphene layer are calculated. The obtained lattice vibrational energy per atom from the classical MC simulation is very close to the energy of a three-dimensional harmonic oscillator 3 kBT . The PIMC simulation shows that quantum effects due to zero-point vibrations are significant for temperatures T energy becomes larger than that of the classical lattice for T zero-point motion causes an increase of 0.53% in the lattice parameter. A minimum in the lattice parameter appears at T ≃500 K. Quantum effects on the atomic vibration amplitude of the graphene lattice and its free energy are investigated.
Energy Technology Data Exchange (ETDEWEB)
Kazlauskas, K.; Tamulatis, G.; Pobedinskas, P.; Zukauskas, A. [Institute of Materials Science and Applied Research, Vilnius University, Sauletekio 9, Build. III, 10222 Vilnius (Lithuania); Huang, Chi-Feng; Cheng, Yung-Chen; Wang, Hsiang-Chen; Yang, C.C. [Graduate Institute of Electro-Optical Engineering, National Taiwan University, 1 Roosevelt Road, Sec. 4, Taipei (Taiwan)
2005-05-01
Application of Monte Carlo simulation of exciton (carrier) hopping for the analysis of the photoluminescence (PL) temperature behavior in In{sub 0.2}Ga{sub 0.8}N/GaN multiple quantum wells is reported. The PL linewidth and peak position measured in the 10-300 K range exhibited a W-shaped and S-shaped temperature behavior, respectively. The W-shaped linewidth dependence was fitted with the results of Monte Carlo simulation, which involved phonon-assisted exciton hopping through energy states confined in the band potential fluctuation minima. The simulation yielded the values of the standard deviation for potential fluctuations within In-rich regions (31 meV), dispersion of the average exciton energy in different regions (29 meV), and the temperature dependence of the band gap, which was found to be in a fair agreement with the photoreflectance data. Our results, which infer in-plane motion of localized excitons within the wells, are consistent with the model of large In-rich regions (''segmented quantum wells'' or ''quantum discs'') with band potential fluctuations inside these regions. (copyright 2005 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Review of quantum Monte Carlo methods and results for Coulombic systems
Energy Technology Data Exchange (ETDEWEB)
Ceperley, D.
1983-01-27
The various Monte Carlo methods for calculating ground state energies are briefly reviewed. Then a summary of the charged systems that have been studied with Monte Carlo is given. These include the electron gas, small molecules, a metal slab and many-body hydrogen.
Quantum Monte Carlo study of the ground state and low-lying excited states of the scandium dimer
Matxain, Jon M.; Rezabal, Elixabete; Lopez, Xabier; Ugalde, Jesus M; Gagliardi, Laura
2008-01-01
A large set of electronic states of scandium dimer has been calculated using high-level theoretical methods such as quantum diffusion Monte Carlo (DMC), complete active space perturbation theory as implemented in GAMESS-US, coupled-cluster singles, doubles, and triples, and density functional theory (DFT). The 3Sigmau and 5Sigmau states are calculated to be close in energy in all cases, but whereas DFT predicts the 5Sigmau state to be the ground state by 0.08 eV, DMC and CASPT2 calculations p...
Calcavecchia, Francesco
2016-01-01
We use the Shadow Wave Function formalism as a convenient model to study the fermion sign problem affecting all projector Quantum Monte Carlo methods in continuum space. We demonstrate that the efficiency of imaginary time projection algorithms decays exponentially with increasing number of particles and/or imaginary-time propagation. Moreover, we derive an analytical expression that connects the localization of the system with the magnitude of the sign problem, illustrating this prediction through some numerical results. Finally, we discuss the fermion sign problem computational complexity and methods for alleviating its severity.
Quantum Monte Carlo study of long-range transverse-field Ising models on the triangular lattice
Humeniuk, Stephan
2016-03-01
Motivated by recent experiments with a Penning ion trap quantum simulator, we perform numerically exact Stochastic Series Expansion quantum Monte Carlo simulations of long-range transverse-field Ising models on a triangular lattice for different decay powers α of the interactions. The phase boundary for the ferromagnet is obtained as a function of α . For antiferromagnetic interactions, there is strong indication that the transverse field stabilizes a clock ordered phase with sublattice magnetization (M ,-M/2 ,-M/2 ) with unsaturated M disorder" similar to the nearest-neighbor antiferromagnet on the triangular lattice. Connecting the known limiting cases of nearest-neighbor and infinite-range interactions, a semiquantitative phase diagram is obtained. Magnetization curves for the ferromagnet for experimentally relevant system sizes and with open boundary conditions are presented.
Toulouse, Julien; Reinhardt, Peter; Hoggan, Philip E; Umrigar, C J
2010-01-01
We report state-of-the-art quantum Monte Carlo calculations of the singlet $n \\to \\pi^*$ (CO) vertical excitation energy in the acrolein molecule, extending the recent study of Bouab\\c{c}a {\\it et al.} [J. Chem. Phys. {\\bf 130}, 114107 (2009)]. We investigate the effect of using a Slater basis set instead of a Gaussian basis set, and of using state-average versus state-specific complete-active-space (CAS) wave functions, with or without reoptimization of the coefficients of the configuration state functions (CSFs) and of the orbitals in variational Monte Carlo (VMC). It is found that, with the Slater basis set used here, both state-average and state-specific CAS(6,5) wave functions give an accurate excitation energy in diffusion Monte Carlo (DMC), with or without reoptimization of the CSF and orbital coefficients in the presence of the Jastrow factor. In contrast, the CAS(2,2) wave functions require reoptimization of the CSF and orbital coefficients to give a good DMC excitation energy. Our best estimates of ...
International Nuclear Information System (INIS)
We present a systematic study of a recently developed ab initio simulation scheme based on molecular dynamics and quantum Monte Carlo. In this approach, a damped Langevin molecular dynamics is employed by using a statistical evaluation of the forces acting on each atom by means of quantum Monte Carlo. This allows the use of an highly correlated wave function parametrized by several variational parameters and describing quite accurately the Born-Oppenheimer energy surface, as long as these parameters are determined at the minimum energy condition. However, in a statistical method both the minimization method and the evaluation of the atomic forces are affected by the statistical noise. In this work, we study systematically the accuracy and reliability of this scheme by targeting the vibrational frequencies of simple molecules such as the water monomer, hydrogen sulfide, sulfur dioxide, ammonia, and phosphine. We show that all sources of systematic errors can be controlled and reliable frequencies can be obtained with a reasonable computational effort. This work provides convincing evidence that this molecular dynamics scheme can be safely applied also to realistic systems containing several atoms
Energy Technology Data Exchange (ETDEWEB)
Luo, Ye, E-mail: xw111luoye@gmail.com; Sorella, Sandro, E-mail: sorella@sissa.it [International School for Advanced Studies (SISSA), and CRS Democritos, CNR-INFM, Via Bonomea 265, I-34136 Trieste (Italy); Zen, Andrea, E-mail: zen.andrea.x@gmail.com [Dipartimento di Fisica, Università di Roma “La Sapienza,” Piazzale Aldo Moro 2, I-00185 Rome (Italy)
2014-11-21
We present a systematic study of a recently developed ab initio simulation scheme based on molecular dynamics and quantum Monte Carlo. In this approach, a damped Langevin molecular dynamics is employed by using a statistical evaluation of the forces acting on each atom by means of quantum Monte Carlo. This allows the use of an highly correlated wave function parametrized by several variational parameters and describing quite accurately the Born-Oppenheimer energy surface, as long as these parameters are determined at the minimum energy condition. However, in a statistical method both the minimization method and the evaluation of the atomic forces are affected by the statistical noise. In this work, we study systematically the accuracy and reliability of this scheme by targeting the vibrational frequencies of simple molecules such as the water monomer, hydrogen sulfide, sulfur dioxide, ammonia, and phosphine. We show that all sources of systematic errors can be controlled and reliable frequencies can be obtained with a reasonable computational effort. This work provides convincing evidence that this molecular dynamics scheme can be safely applied also to realistic systems containing several atoms.
Measure of Bias Cancellation in Fixed-Node Quantum Monte Carlo
Dubecký, Matúš
2016-01-01
We introduce a measure of fixed-node (FN) bias cancellation useful for a priori assessment of FN diffusion Monte Carlo (FN-DMC) energy differences, based on post-Hartree-Fock natural orbital occupation numbers. The proposed quantity reflects the non-equivalency of static correlations in trial wave functions and uncovers the nature of biases observed in some small noncovalent complexes.
Monte Carlo methods and applications for the nuclear shell model
Dean, D. J.; White, J A
1998-01-01
The shell-model Monte Carlo (SMMC) technique transforms the traditional nuclear shell-model problem into a path-integral over auxiliary fields. We describe below the method and its applications to four physics issues: calculations of sdpf- shell nuclei, a discussion of electron-capture rates in pf-shell nuclei, exploration of pairing correlations in unstable nuclei, and level densities in rare earth systems.
Monte Carlo Methods and Applications for the Nuclear Shell Model
International Nuclear Information System (INIS)
The shell-model Monte Carlo (SMMC) technique transforms the traditional nuclear shell-model problem into a path-integral over auxiliary fields. We describe below the method and its applications to four physics issues: calculations of sd-pf-shell nuclei, a discussion of electron-capture rates in pf-shell nuclei, exploration of pairing correlations in unstable nuclei, and level densities in rare earth systems
Kivelson, Steven A.
2016-01-01
This is a "perspective" inspired by the forthcoming article, "What makes the $T_c$ of monolayer FeSe on SrTiO so high: a sign-problem free quantum Monte Carlo study," by Z-X. Li, F. Wang, H. Yao, and D-H. Lee, arXiv:1512.06179.
CPMC-Lab: A Matlab Package for Constrained Path Monte Carlo Calculations
Nguyen, Huy; Shi, Hao; Xu, Jie; Zhang, Shiwei
2014-01-01
We describe CPMC-Lab, a Matlab program for the constrained-path and phaseless auxiliary-field Monte Carlo methods. These methods have allowed applications ranging from the study of strongly correlated models, such as the Hubbard model, to ab initio calculations in molecules and solids. The present package implements the full ground-state constrained-path Monte Carlo (CPMC) method in Matlab with a graphical interface, using the Hubbard model as an example. The package can perform calculations ...
Horváthová, L; Mitas, L; Štich, I
2014-01-01
We present calculations of electronic and magnetic structures of vanadium-benzene multidecker clusters V$_{n}$Bz$_{n+1}$ ($n$ = 1 - 3) using advanced quantum Monte Carlo methods. These and related systems have been identified as prospective spin filters in spintronic applications, assuming that their ground states are half-metallic ferromagnets. Although we find that magnetic properties of these multideckers are consistent with ferromagnetic coupling, their electronic structures do not appear to be half-metallic as previously assumed. In fact, they are ferromagnetic insulators with large and broadly similar $\\uparrow$-/$\\downarrow$-spin gaps. This makes the potential of these and related materials as spin filtering devices very limited, unless they are further modified or functionalized.
Li, Zixiang; Yao, Hong; Wang, Fa; Lee, Dung-Hai
Superconductivity is an emergent phenomena in the sense that the energy scale at which Cooper pairs form is generically much lower than the bare energy scale, namely the electron kinetic energy bandwidth. Addressing the mechanism of Cooper pairing amounts to finding out the effective interaction (or the renormalized interaction) that operates at the low energies. Finding such interaction from the bare microscopic Hamiltonian has not been possible for strong correlated superconductors such as the copper-oxide high temperature superconductor. In fact even one is given the effective interaction, determining its implied electronic instabilities without making any approximation has been a formidable task. Here, we perform sign-free quantum Monte-Carlo simulations to study the antiferromagnetic, superconducting, and the charge density wave instabilities which are ubiquitous in both electron and hole doped cuprates. Our result suggests only after including both the nematic and antiferromagnetic fluctuation, are the observed properties associated with these instabilities reproduced by the theory.
Zen, Andrea; Luo, Ye; Sorella, Sandro; Guidoni, Leonardo
2014-01-01
Diradical molecules are essential species involved in many organic and inorganic chemical reactions. The computational study of their electronic structure is often challenging, because a reliable description of the correlation, and in particular of the static one, requires multi-reference techniques. The Jastrow correlated Antisymmetrized Geminal Power (JAGP) is a compact and efficient wave function ansatz, based on the valence-bond representation, which can be used within Quantum Monte Carlo (QMC) approaches. The AGP part can be rewritten in terms of molecular orbitals, obtaining a multi-determinant expansion with zero-seniority number. In the present work we demonstrate the capability of the JAGP ansatz to correctly describe the electronic structure of two diradical prototypes: the orthogonally twisted ethylene, C2H4, and the methylene, CH2, representing respectively a homosymmetric and heterosymmetric system. On the other hand, we show that the simple ansatz of a Jastrow correlated Single Determinant (JSD)...
Dornheim, Tobias; Sjostrom, Travis; Malone, Fionn D; Foulkes, W M C; Bonitz, Michael
2016-01-01
We perform \\emph{ab initio} quantum Monte Carlo (QMC) simulations of the warm dense uniform electron gas in the thermodynamic limit. By combining QMC data with linear response theory we are able to remove finite-size errors from the potential energy over the entire warm dense regime, overcoming the deficiencies of the existing finite-size corrections by Brown \\emph{et al.}~[PRL \\textbf{110}, 146405 (2013)]. Extensive new QMC results for up to $N=1000$ electrons enable us to compute the potential energy $V$ and the exchange-correlation free energy $F_{xc}$ of the macroscopic electron gas with an unprecedented accuracy of $|\\Delta V|/|V|, |\\Delta F_{xc}|/|F|_{xc} \\sim 10^{-3}$. A comparison of our new data to the recent parametrization of $F_{xc}$ by Karasiev {\\em et al.} [PRL {\\bf 112}, 076403 (2014)] reveals significant inaccuracies of the latter.
Zero-Variance Zero-Bias Principle for Observables in quantum Monte Carlo: Application to Forces
Assaraf, R
2003-01-01
A simple and stable method for computing accurate expectation values of observable with Variational Monte Carlo (VMC) or Diffusion Monte Carlo (DMC) algorithms is presented. The basic idea consists in replacing the usual ``bare'' estimator associated with the observable by an improved or ``renormalized'' estimator. Using this estimator more accurate averages are obtained: Not only the statistical fluctuations are reduced but also the systematic error (bias) associated with the approximate VMC or (fixed-node) DMC probability densities. It is shown that improved estimators obey a Zero-Variance Zero-Bias (ZVZB) property similar to the usual Zero-Variance Zero-Bias property of the energy with the local energy as improved estimator. Using this property improved estimators can be optimized and the resulting accuracy on expectation values may reach the remarkable accuracy obtained for total energies. As an important example, we present the application of our formalism to the computation of forces in molecular system...
Hydrogen dissociation on the Mg(0001) surface from quantum Monte Carlo calculations
Pozzo, M.; Alfe`, D.
2008-01-01
We have used diffusion Monte Carlo (DMC) simulations to calculate the energy barrier for H$_2$ dissociation on the Mg(0001) surface. The calculations employ pseudopotentials and systematically improvable B-spline basis sets to expand the single particle orbitals used to construct the trial wavefunctions. Extensive tests on system size, time step, and other sources of errors, performed on periodically repeated systems of up to 550 atoms, show that all these errors together can be reduced to $\\...
Energy Technology Data Exchange (ETDEWEB)
Bauer, Thilo; Jäger, Christof M. [Department of Chemistry and Pharmacy, Computer-Chemistry-Center and Interdisciplinary Center for Molecular Materials, Friedrich-Alexander-Universität Erlangen-Nürnberg, Nägelsbachstrasse 25, 91052 Erlangen (Germany); Jordan, Meredith J. T. [School of Chemistry, University of Sydney, Sydney, NSW 2006 (Australia); Clark, Timothy, E-mail: tim.clark@fau.de [Department of Chemistry and Pharmacy, Computer-Chemistry-Center and Interdisciplinary Center for Molecular Materials, Friedrich-Alexander-Universität Erlangen-Nürnberg, Nägelsbachstrasse 25, 91052 Erlangen (Germany); Centre for Molecular Design, University of Portsmouth, Portsmouth PO1 2DY (United Kingdom)
2015-07-28
We have developed a multi-agent quantum Monte Carlo model to describe the spatial dynamics of multiple majority charge carriers during conduction of electric current in the channel of organic field-effect transistors. The charge carriers are treated by a neglect of diatomic differential overlap Hamiltonian using a lattice of hydrogen-like basis functions. The local ionization energy and local electron affinity defined previously map the bulk structure of the transistor channel to external potentials for the simulations of electron- and hole-conduction, respectively. The model is designed without a specific charge-transport mechanism like hopping- or band-transport in mind and does not arbitrarily localize charge. An electrode model allows dynamic injection and depletion of charge carriers according to source-drain voltage. The field-effect is modeled by using the source-gate voltage in a Metropolis-like acceptance criterion. Although the current cannot be calculated because the simulations have no time axis, using the number of Monte Carlo moves as pseudo-time gives results that resemble experimental I/V curves.
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Bertini, Luca [Dipartimento di Chimica Fisica ed Elettrochimica, Universita di Milano, Milan (Italy)]. E-mail: bert@csrsrc.mi.cnr.it; Mella, Massimo [Dipartimento di Chimica Fisica ed Elettrochimica, Universita di Milano, Milan (Italy)]. E-mail: Massimo.Mella@unimi.it; Bressanini, Dario [Dipartimento di Scienze Chimiche, Fisiche e Matematiche, Universita dell' Insubria, Como (Italy)]. E-mail: Dario.Bressanini@uninsubria.it; Morosi, Gabriele [Dipartimento di Scienze Chimiche, Fisiche e Matematiche, Universita dell' Insubria, Como (Italy)]. E-mail: Gabriele.Morosi@uninsubria.it
2001-02-14
We present a new form of explicitly correlated wavefunction whose parameters are mainly linear, to circumvent the problem of the optimization of a large number of nonlinear parameters usually encountered with basis sets of explicitly correlated wavefunctions. With this trial wavefunction we have succeeded in minimizing the energy instead of the variance of the local energy, as is more common in quantum Monte Carlo methods. We have applied this wavefunction to the calculation of the energies of Be {sup 3}P (1s{sup 2}2p{sup 2}) and Be{sup -} {sup 4}S{sup o} (1s{sup 2}2p{sup 3}) by variational and diffusion Monte Carlo methods. The results compare favourably with those obtained by different types of explicitly correlated trial wavefunction already described in the literature. The energies obtained are improved with respect to the best variational ones found in the literature, and within one standard deviation of the estimated non-relativistic limits. (author)
International Nuclear Information System (INIS)
We have developed a multi-agent quantum Monte Carlo model to describe the spatial dynamics of multiple majority charge carriers during conduction of electric current in the channel of organic field-effect transistors. The charge carriers are treated by a neglect of diatomic differential overlap Hamiltonian using a lattice of hydrogen-like basis functions. The local ionization energy and local electron affinity defined previously map the bulk structure of the transistor channel to external potentials for the simulations of electron- and hole-conduction, respectively. The model is designed without a specific charge-transport mechanism like hopping- or band-transport in mind and does not arbitrarily localize charge. An electrode model allows dynamic injection and depletion of charge carriers according to source-drain voltage. The field-effect is modeled by using the source-gate voltage in a Metropolis-like acceptance criterion. Although the current cannot be calculated because the simulations have no time axis, using the number of Monte Carlo moves as pseudo-time gives results that resemble experimental I/V curves
Sharma, Peter; Abraham, J. B. S.; Ten Eyck, G.; Childs, K. D.; Bielejec, E.; Carroll, M. S.
Detection of single ion implantation within a nanostructure is necessary for the high yield fabrication of implanted donor-based quantum computing architectures. Single ion Geiger mode avalanche (SIGMA) diodes with a laterally integrated nanostructure capable of forming a quantum dot were fabricated and characterized using photon pulses. The detection efficiency of this design was measured as a function of wavelength, lateral position, and for varying delay times between the photon pulse and the overbias detection window. Monte Carlo simulations based only on the random diffusion of photo-generated carriers and the geometrical placement of the avalanche region agrees qualitatively with device characterization. Based on these results, SIGMA detection efficiency appears to be determined solely by the diffusion of photo-generated electron-hole pairs into a buried avalanche region. Device performance is then highly dependent on the uniformity of the underlying silicon substrate and the proximity of photo-generated carriers to the silicon-silicon dioxide interface, which are the most important limiting factors for reaching the single ion detection limit with SIGMA detectors. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under Contract DE-AC04-94AL85000.
Pedrocchi, Fabio L.; Bonesteel, N. E.; DiVincenzo, David P.
2015-09-01
The Majorana code is an example of a stabilizer code where the quantum information is stored in a system supporting well-separated Majorana bound states (MBSs). We focus on one-dimensional realizations of the Majorana code, as well as networks of such structures, and investigate their lifetime when coupled to a parity-preserving thermal environment. We apply the Davies prescription, a standard method that describes the basic aspects of a thermal environment, and derive a master equation in the Born-Markov limit. We first focus on a single wire with immobile MBSs and perform error correction to annihilate thermal excitations. In the high-temperature limit, we show both analytically and numerically that the lifetime of the Majorana qubit grows logarithmically with the size of the wire. We then study a trijunction with four MBSs when braiding is executed. We study the occurrence of dangerous error processes that prevent the lifetime of the Majorana code from growing with the size of the trijunction. The origin of the dangerous processes is the braiding itself, which separates pairs of excitations and renders the noise nonlocal; these processes arise from the basic constraints of moving MBSs in one-dimensional (1D) structures. We confirm our predictions with Monte Carlo simulations in the low-temperature regime, i.e., the regime of practical relevance. Our results put a restriction on the degree of self-correction of this particular 1D topological quantum computing architecture.
Ab initio quantum Monte Carlo simulations of the uniform electron gas without fixed nodes
Groth, S.; Schoof, T.; Dornheim, T.; Bonitz, M.
2016-02-01
The uniform electron gas (UEG) at finite temperature is of key relevance for many applications in the warm dense matter regime, e.g., dense plasmas and laser excited solids. Also, the quality of density functional theory calculations crucially relies on the availability of accurate data for the exchange-correlation energy. Recently, results for N =33 spin-polarized electrons at high density, rs=r ¯/aB≲4 , and low temperature have been obtained with the configuration path integral Monte Carlo (CPIMC) method [T. Schoof et al., Phys. Rev. Lett. 115, 130402 (2015), 10.1103/PhysRevLett.115.130402]. To achieve these results, the original CPIMC algorithm [T. Schoof et al., Contrib. Plasma Phys. 51, 687 (2011), 10.1002/ctpp.201100012] had to be further optimized to cope with the fermion sign problem (FSP). It is the purpose of this paper to give detailed information on the manifestation of the FSP in CPIMC simulations of the UEG and to demonstrate how it can be turned into a controllable convergence problem. In addition, we present new thermodynamic results for higher temperatures. Finally, to overcome the limitations of CPIMC towards strong coupling, we invoke an independent method—the recently developed permutation blocking path integral Monte Carlo approach [T. Dornheim et al., J. Chem. Phys. 143, 204101 (2015), 10.1063/1.4936145]. The combination of both approaches is able to yield ab initio data for the UEG over the entire density range, above a temperature of about one half of the Fermi temperature. Comparison with restricted path integral Monte Carlo data [E. W. Brown et al., Phys. Rev. Lett. 110, 146405 (2013), 10.1103/PhysRevLett.110.146405] allows us to quantify the systematic error arising from the free particle nodes.
Härtle, R.; Cohen, G.; Reichman, D. R.; Millis, A. J.
2015-08-01
We give a detailed comparison of the hierarchical quantum master equation (HQME) method to a continuous-time quantum Monte Carlo (CT-QMC) approach, assessing the usability of these numerically exact schemes as impurity solvers in practical nonequilibrium calculations. We review the main characteristics of the methods and discuss the scaling of the associated numerical effort. We substantiate our discussion with explicit numerical results for the nonequilibrium transport properties of a single-site Anderson impurity. The numerical effort of the HQME scheme scales linearly with the simulation time but increases (at worst exponentially) with decreasing temperature. In contrast, CT-QMC is less restricted by temperature at short times, but in general the cost of going to longer times is also exponential. After establishing the numerical exactness of the HQME scheme, we use it to elucidate the influence of different ways to induce transport through the impurity on the initial dynamics, discuss the phenomenon of coherent current oscillations, known as current ringing, and explain the nonmonotonic temperature dependence of the steady-state magnetization as a result of competing broadening effects. We also elucidate the pronounced nonlinear magnetization dynamics, which appears on intermediate time scales in the presence of an asymmetric coupling to the electrodes.
Tubman, Norm; Hammes-Schiffer, Sharon; Ceperley, David
2016-01-01
Simulating nonadiabatic effects with many-body wave function approaches is an open field with many challenges. Recent interest has been driven by new algorithmic developments and improved theoretical understanding of properties unique to electron-ion wave functions. Fixed-node diffusion Monte Caro is one technique that has shown promising results for simulating electron-ion systems. In particular, we focus on the CH molecule for which previous results suggested a relatively significant contribution to the energy from nonadiabatic effects. We propose a new wave function ansatz for diatomic systems which involves interpolating the determinant coefficients calculated from configuration interaction methods. We find this to be an improvement beyond previous wave function forms that have been considered. The calculated nonadiabatic contribution to the energy in the CH molecule is reduced compared to our previous results, but still remains the largest among the molecules under consideration.
Quantum Monte Carlo simulations of the one-dimensional extended Hubbard model
International Nuclear Information System (INIS)
We report preliminary results of an investigation of the thermodynamic properties of the extended Hubbard model in one- dimension, calculated with the world-line Monte Carlo method described by Hirsch et al. With strictly continuous world-lines, we are able to measure the expectation of operators that conserve fermion number locally, such as the energy and (spatial) occupation number. By permitting the world-lines to be ''broken'' stochastically, we may also measure the expectation of operators that conserve fermion number only globally, such as the single-particle Green's function. For a 32 site lattice we present preliminary calculations of the average electron occupancy as a function of wavenumber when U = 4, V = 0 and β = 16. For a half-filled band we find no indications of a Fermi surface. Slightly away from half-filling, we find Fermi-surface-like behavior similar to that found in other numerical investigations. 8 refs., 3 figs
Quantum Monte Carlo calculation of the binding energy of the beryllium dimer
International Nuclear Information System (INIS)
The accurate calculation of the binding energy of the beryllium dimer is a challenging theoretical problem. In this study, the binding energy of Be2 is calculated using the diffusion Monte Carlo (DMC) method, using single Slater determinant and multiconfigurational trial functions. DMC calculations using single-determinant trial wave functions of orbitals obtained from density functional theory calculations overestimate the binding energy, while DMC calculations using Hartree-Fock or CAS(4,8), complete active space trial functions significantly underestimate the binding energy. In order to obtain an accurate value of the binding energy of Be2 from DMC calculations, it is necessary to employ trial functions that include excitations outside the valence space. Our best estimate DMC result for the binding energy of Be2, obtained by using configuration interaction trial functions and extrapolating in the threshold for the configurations retained in the trial function, is 908 cm−1, only slightly below the 935 cm−1 value derived from experiment
Zen, Andrea; Sorella, Sandro; Guidoni, Leonardo
2013-01-01
Quantum Monte Carlo methods are accurate and promising many body techniques for electronic structure calculations which, in the last years, are encountering a growing interest thanks to their favorable scaling with the system size and their efficient parallelization, particularly suited for the modern high performance computing facilities. The ansatz of the wave function and its variational flexibility are crucial points for both the accurate description of molecular properties and the capabilities of the method to tackle large systems. In this paper, we extensively analyze, using different variational ansatzes, several properties of the water molecule, namely: the total energy, the dipole and quadrupole momenta, the ionization and atomization energies, the equilibrium configuration, and the harmonic and fundamental frequencies of vibration. The investigation mainly focuses on variational Monte Carlo calculations, although several lattice regularized diffusion Monte Carlo calculations are also reported. Throu...
International Nuclear Information System (INIS)
Studying the thermodynamics of gases, lattices and other statistical systems via numerical simulations requires the mapping of energy density, pressure and other quantities as functions of temperature. Of special importance is the accurate mapping near and at phase transitions, where discontinuities are present and difficult to measure with a limited number of computerized simulations. This is particularly true for Quantum Chromodynamics, the theory of quarks and gluons, which is known to have a first-order phase transition at a temperature of about 150 MeV. This paper shows that by using the recently proposed method of density of states, one can optimize the information obtained from these limited simulations with supercomputers in order to obtain in the worst cases the derivative of the thermodynamical functions, and in the best cases, their entire curve over a wide range of temperatures
Y. Lin; Cohen, R E; Stackhouse, S.; Driver, K. P.; Militzer, B.; Shulenburger, L.; J. Kim
2014-01-01
We have performed quantum Monte Carlo (QMC) simulations and density functional theory calculations to study the equations of state of MgSiO3 perovskite (Pv, bridgmanite) and post-perovskite (PPv) up to the pressure and temperature conditions of the base of Earth's lower mantle. The ground-state energies were derived using QMC simulations and the temperature-dependent Helmholtz free energies were calculated within the quasiharmonic approximation and density functional perturbation theory. The ...
Barborini, Matteo; Guidoni, Leonardo
2012-12-01
Quantum Monte Carlo (QMC) methods are used to investigate the intramolecular reaction pathways of 1,3-butadiene. The ground state geometries of the three conformers s-trans, s-cis, and gauche, as well as the cyclobutene structure are fully optimised at the variational Monte Carlo (VMC) level, obtaining an excellent agreement with the experimental results and other quantum chemistry high level calculations. Transition state geometries are also estimated at the VMC level for the s-trans to gauche torsion barrier of 1,3-butadiene and for the conrotatory ring opening of cyclobutene to the gauche-1,3-butadiene conformer. The energies of the conformers and the reaction barriers are calculated at both variational and diffusional Monte Carlo levels providing a precise picture of the potential energy surface of 1,3-butadiene and supporting one of the two model profiles recently obtained by Raman spectroscopy [Boopalachandran et al., J. Phys. Chem. A 115, 8920 (2011), 10.1021/jp2051596]. Considering the good scaling of QMC techniques with the system's size, our results also demonstrate how variational Monte Carlo calculations can be applied in the future to properly investigate the reaction pathways of large and correlated molecular systems.
International Nuclear Information System (INIS)
The quantum Monte Carlo (QMC) technique is used to generate accurate energy benchmarks for methane-water clusters containing a single methane monomer and up to 20 water monomers. The benchmarks for each type of cluster are computed for a set of geometries drawn from molecular dynamics simulations. The accuracy of QMC is expected to be comparable with that of coupled-cluster calculations, and this is confirmed by comparisons for the CH4-H2O dimer. The benchmarks are used to assess the accuracy of the second-order Møller-Plesset (MP2) approximation close to the complete basis-set limit. A recently developed embedded many-body technique is shown to give an efficient procedure for computing basis-set converged MP2 energies for the large clusters. It is found that MP2 values for the methane binding energies and the cohesive energies of the water clusters without methane are in close agreement with the QMC benchmarks, but the agreement is aided by partial cancelation between 2-body and beyond-2-body errors of MP2. The embedding approach allows MP2 to be applied without loss of accuracy to the methane hydrate crystal, and it is shown that the resulting methane binding energy and the cohesive energy of the water lattice agree almost exactly with recently reported QMC values
Energy Technology Data Exchange (ETDEWEB)
Gillan, M. J., E-mail: m.gillan@ucl.ac.uk [London Centre for Nanotechnology, University College London, Gordon St., London WC1H 0AH (United Kingdom); Department of Physics and Astronomy, University College London, Gower St., London WC1E 6BT (United Kingdom); Thomas Young Centre, University College London, Gordon St., London WC1H 0AH (United Kingdom); Alfè, D. [London Centre for Nanotechnology, University College London, Gordon St., London WC1H 0AH (United Kingdom); Department of Physics and Astronomy, University College London, Gower St., London WC1E 6BT (United Kingdom); Thomas Young Centre, University College London, Gordon St., London WC1H 0AH (United Kingdom); Department of Earth Sciences, University College London, Gower St., London WC1E 6BT (United Kingdom); Manby, F. R. [Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS (United Kingdom)
2015-09-14
The quantum Monte Carlo (QMC) technique is used to generate accurate energy benchmarks for methane-water clusters containing a single methane monomer and up to 20 water monomers. The benchmarks for each type of cluster are computed for a set of geometries drawn from molecular dynamics simulations. The accuracy of QMC is expected to be comparable with that of coupled-cluster calculations, and this is confirmed by comparisons for the CH{sub 4}-H{sub 2}O dimer. The benchmarks are used to assess the accuracy of the second-order Møller-Plesset (MP2) approximation close to the complete basis-set limit. A recently developed embedded many-body technique is shown to give an efficient procedure for computing basis-set converged MP2 energies for the large clusters. It is found that MP2 values for the methane binding energies and the cohesive energies of the water clusters without methane are in close agreement with the QMC benchmarks, but the agreement is aided by partial cancelation between 2-body and beyond-2-body errors of MP2. The embedding approach allows MP2 to be applied without loss of accuracy to the methane hydrate crystal, and it is shown that the resulting methane binding energy and the cohesive energy of the water lattice agree almost exactly with recently reported QMC values.
Busemeyer, Brian; Dagrada, Mario; Sorella, Sandro; Casula, Michele; Wagner, Lucas K.
2016-07-01
Resolving the interplay between magnetic interactions and structural properties in strongly correlated materials through a quantitatively accurate approach has been a major challenge in condensed-matter physics. Here we apply highly accurate first-principles quantum Monte Carlo (QMC) techniques to obtain structural and magnetic properties of the iron selenide (FeSe) superconductor under pressure. Where comparable, the computed properties are very close to the experimental values. Of potential ordered magnetic configurations, collinear spin configurations are the most energetically favorable over the explored pressure range. They become nearly degenerate in energy with bicollinear spin orderings at around 7 GPa, when the experimental critical temperature Tc is the highest. On the other hand, ferromagnetic, checkerboard, and staggered dimer configurations become relatively higher in energy as the pressure increases. The behavior under pressure is explained by an analysis of the local charge compressibility and the orbital occupation as described by the QMC many-body wave function, which reveals how spin, charge, and orbital degrees of freedom are strongly coupled in this compound. This remarkable pressure evolution suggests that stripelike magnetic fluctuations may be responsible for the enhanced Tc in FeSe and that higher Tc is associated with nearness to a crossover between collinear and bicollinear ordering.
Santana, Juan A.; Krogel, Jaron T.; Kent, Paul R. C.; Reboredo, Fernando A.
2016-05-01
We have applied the diffusion quantum Monte Carlo (DMC) method to calculate the cohesive energy and the structural parameters of the binary oxides CaO, SrO, BaO, Sc2O3, Y2O3, and La2O3. The aim of our calculations is to systematically quantify the accuracy of the DMC method to study this type of metal oxides. The DMC results were compared with local, semi-local, and hybrid Density Functional Theory (DFT) approximations as well as with experimental measurements. The DMC method yields cohesive energies for these oxides with a mean absolute deviation from experimental measurements of 0.18(2) eV, while with local, semi-local, and hybrid DFT approximations, the deviation is 3.06, 0.94, and 1.23 eV, respectively. For lattice constants, the mean absolute deviations in DMC, local, semi-local, and hybrid DFT approximations are 0.017(1), 0.07, 0.05, and 0.04 Å, respectively. DMC is a highly accurate method, outperforming the DFT approximations in describing the cohesive energies and structural parameters of these binary oxides.
Gillan, M J; Alfè, D; Manby, F R
2015-09-14
The quantum Monte Carlo (QMC) technique is used to generate accurate energy benchmarks for methane-water clusters containing a single methane monomer and up to 20 water monomers. The benchmarks for each type of cluster are computed for a set of geometries drawn from molecular dynamics simulations. The accuracy of QMC is expected to be comparable with that of coupled-cluster calculations, and this is confirmed by comparisons for the CH4-H2O dimer. The benchmarks are used to assess the accuracy of the second-order Møller-Plesset (MP2) approximation close to the complete basis-set limit. A recently developed embedded many-body technique is shown to give an efficient procedure for computing basis-set converged MP2 energies for the large clusters. It is found that MP2 values for the methane binding energies and the cohesive energies of the water clusters without methane are in close agreement with the QMC benchmarks, but the agreement is aided by partial cancelation between 2-body and beyond-2-body errors of MP2. The embedding approach allows MP2 to be applied without loss of accuracy to the methane hydrate crystal, and it is shown that the resulting methane binding energy and the cohesive energy of the water lattice agree almost exactly with recently reported QMC values. PMID:26374005
Quantum Monte Carlo simulation of antiferromagnetic spin ladder (C5H12N)2CuBr4
Freitas, Augusto S.
2016-07-01
In this paper I present a Quantum Monte Carlo (QMC) study of the magnetic properties of an antiferromagnetic spin ladder (C5H12N)2CuBr4. This compound is the prototype of the Heisenberg model for a two leg spin ladder in the presence of an external magnetic field. The susceptibility phase diagram has a rounded peak in the vicinity of T=7.4 K, obeys Troyer's law for low temperatures, and Curie's law for high temperatures. I also study the susceptibility diagram in low temperatures and I found the spin gap Δ=9.26 K, in good concordance with the experimental value, 9.5 K. In high field, I present a diagram of magnetization as a function of temperature. In the vicinity of a critical field, Hci, the magnetization scales with T1/2 and this result was found also in the QMC simulation. In all the results, there is a very good concordance with the experimental data. I also show in this paper that the spin gap is null and the susceptibility is proportional to T for low temperatures when relatively high values of the ladders' coupling is taken in account.
Han, Mancheon; Lee, Choong-Ki; Choi, Hyoung Joon
Hybridization-expansion continuous-time quantum Monte Carlo (CT-HYB) is a popular approach in real material researches because it allows to deal with non-density-density-type interaction. In the conventional CT-HYB, we measure Green's function and find the self energy from the Dyson equation. Because one needs to compute the inverse of the statistical data in this approach, obtained self energy is very sensitive to statistical noise. For that reason, the measurement is not reliable except for low frequencies. Such an error can be suppressed by measuring a special type of higher-order correlation function and is implemented for density-density-type interaction. With the help of the recently reported worm-sampling measurement, we developed an improved self energy measurement scheme which can be applied to any type of interactions. As an illustration, we calculated the self energy for the 3-orbital Hubbard-Kanamori-type Hamiltonian with our newly developed method. This work was supported by NRF of Korea (Grant No. 2011-0018306) and KISTI supercomputing center (Project No. KSC-2015-C3-039)
Many-body ab initio diffusion quantum Monte Carlo applied to the strongly correlated oxide NiO
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Mitra, Chandrima; Krogel, Jaron T.; Santana, Juan A.; Reboredo, Fernando A., E-mail: reboredofa@ornl.gov [Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (United States)
2015-10-28
We present a many-body diffusion quantum Monte Carlo (DMC) study of the bulk and defect properties of NiO. We find excellent agreement with experimental values, within 0.3%, 0.6%, and 3.5% for the lattice constant, cohesive energy, and bulk modulus, respectively. The quasiparticle bandgap was also computed, and the DMC result of 4.72 (0.17) eV compares well with the experimental value of 4.3 eV. Furthermore, DMC calculations of excited states at the L, Z, and the gamma point of the Brillouin zone reveal a flat upper valence band for NiO, in good agreement with Angle Resolved Photoemission Spectroscopy results. To study defect properties, we evaluated the formation energies of the neutral and charged vacancies of oxygen and nickel in NiO. A formation energy of 7.2 (0.15) eV was found for the oxygen vacancy under oxygen rich conditions. For the Ni vacancy, we obtained a formation energy of 3.2 (0.15) eV under Ni rich conditions. These results confirm that NiO occurs as a p-type material with the dominant intrinsic vacancy defect being Ni vacancy.
International Nuclear Information System (INIS)
We compute two- and three-body cluster functions that describe contributions of composite entities, like hydrogen atoms, ions H−, H2+, and helium atoms, and also charge-charge and atom-charge interactions, to the equation of state of a hydrogen-helium mixture at low density. A cluster function has the structure of a truncated virial coefficient and behaves, at low temperatures, like a usual partition function for the composite entity. Our path integral Monte Carlo calculations use importance sampling to sample efficiently the cluster partition functions even at low temperatures where bound state contributions dominate. We also employ a new and efficient adaptive discretization scheme that allows one not only to eliminate Coulomb divergencies in discretized path integrals, but also to direct the computational effort where particles are close and thus strongly interacting. The numerical results for the two-body function agree with the analytically known quantum second virial coefficient. The three-body cluster functions are compared at low temperatures with familiar partition functions for composite entities
Phase Boundary between MgSiO3 Perovskite and Post-perovskite from Quantum Monte Carlo Simulations
Lin, Yangzheng; Cohen, R. E.; Stackhouse, Stephen; Driver, Kevin P.; Militzer, Burkhard; Shulenburger, Luke; Kim, Jeongnim
2015-03-01
Accurate prediction of the phase boundary between perovskite (pv) and post-perovskite (ppv) phases of MgSiO3 is important to explain many unusual properties of the Earth's D'' layer, such as lateral variations in the depth of the observed seismic discontinuity and seismic anisotropy. We have performed quantum Monte Carlo (QMC) simulations with the QMCPACK code on GPU clusters to obtain the ground state equation of state. Density functional perturbation theory (DFPT) computations were performed to obtain the thermal pressure within quasiharmonic lattice dynamics. The equations of state for both phases of MgSiO3 and their phase boundary from our QMC simulations agree well with experiment results and better than previous DFT calculations. Double-crossing of the pv-ppv boundary along Earth's geotherm depends on the effects of iron on the transition. Computations were performed on XSEDE machine Stampede, and on the Oak Ridge Leadership Computing Facility (OLCF) machine Titan from INCITE program. This work is supported by NSF.
Viel, Alexandra; Coutinho-Neto, Maurício D.; Manthe, Uwe
2007-01-01
Quantum dynamics calculations of the ground state tunneling splitting and of the zero point energy of malonaldehyde on the full dimensional potential energy surface proposed by Yagi et al. [J. Chem. Phys. 1154, 10647 (2001)] are reported. The exact diffusion Monte Carlo and the projection operator imaginary time spectral evolution methods are used to compute accurate benchmark results for this 21-dimensional ab initio potential energy surface. A tunneling splitting of 25.7±0.3cm-1 is obtained, and the vibrational ground state energy is found to be 15122±4cm-1. Isotopic substitution of the tunneling hydrogen modifies the tunneling splitting down to 3.21±0.09cm-1 and the vibrational ground state energy to 14385±2cm-1. The computed tunneling splittings are slightly higher than the experimental values as expected from the potential energy surface which slightly underestimates the barrier height, and they are slightly lower than the results from the instanton theory obtained using the same potential energy surface.
Energy Technology Data Exchange (ETDEWEB)
Kazlauskas, K.; Tamulatis, G.; Jursenas, S.; Zukauskas, A. [Institute of Materials Science and Applied Research, Vilnius University, Sauletekio 9, Build. III, 10222 Vilnius (Lithuania); Springis, M. [Institute of Solid State Physics, University of Latvia, Kengaraga iela 8, 1063 Riga (Latvia); Cheng, Yung-Chen; Wang, Hsiang-Chen; Huang, Chi-Feng; Yang, C.C. [Graduate Institute of Electro-Optical Engineering, National Taiwan University, 1 Roosevelt Road, Sec. 4, Taipei (Taiwan)
2005-02-01
Monte Carlo simulation approach based on exciton hopping through randomly distributed localized states is proposed for quantitative characterization of the band edge of In{sub x}Ga{sub 1-x}N/GaN multiple quantum wells with different indium content (x{approx}0.22-0.27). The band edge dynamics is investigated in the 10-300 K range by analyzing the measured S- and W-shaped temperature behavior of the photoluminescence peak position and linewidth, respectively. The simulation of the W-shaped temperature dependence using double-scaled potential profile model enabled us to estimate the scale of the potential fluctuations due to variation of indium content inside and among In-rich regions formed in InGaN alloy. Increased indium content in InGaN alloy resulted in an increase of the both scales of the potential fluctuations. Moreover, the temperature dependence of the exciton energy was reconstructed and compared with that obtained from the photoreflectance measurements. The density of localized states used in the simulations was in agreement with the photoluminescence excitation data. (copyright 2005 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Many-body ab initio diffusion quantum Monte Carlo applied to the strongly correlated oxide NiO
International Nuclear Information System (INIS)
We present a many-body diffusion quantum Monte Carlo (DMC) study of the bulk and defect properties of NiO. We find excellent agreement with experimental values, within 0.3%, 0.6%, and 3.5% for the lattice constant, cohesive energy, and bulk modulus, respectively. The quasiparticle bandgap was also computed, and the DMC result of 4.72 (0.17) eV compares well with the experimental value of 4.3 eV. Furthermore, DMC calculations of excited states at the L, Z, and the gamma point of the Brillouin zone reveal a flat upper valence band for NiO, in good agreement with Angle Resolved Photoemission Spectroscopy results. To study defect properties, we evaluated the formation energies of the neutral and charged vacancies of oxygen and nickel in NiO. A formation energy of 7.2 (0.15) eV was found for the oxygen vacancy under oxygen rich conditions. For the Ni vacancy, we obtained a formation energy of 3.2 (0.15) eV under Ni rich conditions. These results confirm that NiO occurs as a p-type material with the dominant intrinsic vacancy defect being Ni vacancy
Hu, Wen-Jun; Gong, Shou-Shu; Sheng, D. N.
2016-08-01
By using Gutzwiller projected fermionic wave functions and variational Monte Carlo technique, we study the spin-1 /2 Heisenberg model with the first-neighbor (J1), second-neighbor (J2), and additional scalar chiral interaction JχSi.(Sj×Sk) on the triangular lattice. In the nonmagnetic phase of the J1-J2 triangular model with 0.08 ≲J2/J1≲0.16 , recent density-matrix renormalization group (DMRG) studies [Zhu and White, Phys. Rev. B 92, 041105(R) (2015), 10.1103/PhysRevB.92.041105 and Hu, Gong, Zhu, and Sheng, Phys. Rev. B 92, 140403(R) (2015), 10.1103/PhysRevB.92.140403] find a possible gapped spin liquid with the signal of a competition between a chiral and a Z2 spin liquid. Motivated by the DMRG results, we consider the chiral interaction JχSi.(Sj×Sk) as a perturbation for this nonmagnetic phase. We find that with growing Jχ, the gapless U(1) Dirac spin liquid, which has the best variational energy for Jχ=0 , exhibits the energy instability towards a gapped spin liquid with nontrivial magnetic fluxes and nonzero chiral order. We calculate topological Chern number and ground-state degeneracy, both of which identify this flux state as the chiral spin liquid with fractionalized Chern number C =1 /2 and twofold topological degeneracy. Our results indicate a positive direction to stabilize a chiral spin liquid near the nonmagnetic phase of the J1-J2 triangular model.
International Nuclear Information System (INIS)
Comparison of the Monte Carlo and rate equation methods as applied to the study of electron transport in a mid-infrared quantum cascade laser structure initially proposed by Page et al (2001 Appl. Phys. Lett. 78 3529) is presented for a range of realistic injector doping levels. An analysis of the difference between these two methods is given. It is suggested that justified approximations of the rate equation method, originated by imposing Fermi–Dirac statistics and the same electron effective temperature for each of the energy sub-bands, can be interpreted as partial inclusion of electron–electron interactions. Results of the rate equation method may be used as good initial conditions for a more precise Monte Carlo simulation. An algorithm combining rate equation and Monte Carlo simulations is examined. A reasonable agreement between the introduced method and a fully self-consistent resolution of Monte Carlo and Schrödinger coupled with Poisson equations is demonstrated. The computation time may be reduced when the combined algorithm is used. (paper)
Site, L Delle
2014-01-01
The constrained-search principle introduced by Levy and Lieb, is proposed as a practical, though conceptually rigorous, link between Density Functional Theory (DFT) and Quantum Monte Carlo (QMC). The resulting numerical protocol realizes in practice the implicit key statement of DFT: "Given the three dimensional electron density of the ground state of a system of N electrons with external potential v(r) it is possible to find the corresponding 3N-dimensional wavefunction of ground state." From a numerical point of view, the proposed protocol can be employed to speed up the QMC procedure by employing DFT densities as a pre-selection criterion for the sampling of wavefunctions.
International Nuclear Information System (INIS)
We develop a formalism and present an algorithm for optimization of the trial wave-function used in fixed-node diffusion quantum Monte Carlo (DMC) methods. The formalism is based on the DMC mixed estimator of the ground state probability density. We take advantage of a basic property of the walker configuration distribution function generated in a DMC calculation, to (i) project-out a multi-determinant expansion of the fixed node ground state wave-function and (ii) to define a cost function that relates the interacting-ground-state-fixed-node and the non-interacting-trial wave-functions. We argue in favor of the conjecture that removing the kink of the fixed-node ground-state wave-function at the node improves the resulting wave-function nodal structure. If this conjecture is valid, then the noise in the fixed-noded wave function resulting from finite sampling would play a beneficial role, allowing the nodes to adjust towards the ones of the exact many-body ground state in a simulated annealing-like process. Based on these conjectures, we propose a method to improve both single determinant and multi-determinant expressions of the trial wave-function that can be generalized to other wave-function forms such as pfaffians. We test the method in a model system where a near analytical solution can be found. Comparing the DMC calculations with the exact solutions, we find that the trial wave-function is systematically improved. The overlap of the optimized trial wave-function and the exact ground state converges to 100% even starting from wave-functions orthogonal to the exact ground state. Similarly, the DMC total energy and density converges to the exact solutions for the model. In the optimization process we find an approximation optimal effective non-interacting density-functional-like nodal potential whose existence was predicted in a previous publication (Phys. Rev. B 77 245110 (2008)). Tests of the method are extended to a model system with a full Coulomb
Energy Technology Data Exchange (ETDEWEB)
Matuttis, Hans-Georg [Dep. of Mech. Engineering and Intelligent Systems, The Univ. of Electro-Communications, Tokyo (Japan); Wang, Xiaoxing [Schlumberger K.K. Technology Group (Japan)
2015-03-10
Decomposition methods of the Suzuki-Trotter type of various orders have been derived in different fields. Applying them both to classical ordinary differential equations (ODEs) and quantum systems allows to judge their effectiveness and gives new insights for many body quantum mechanics where reference data are scarce. Further, based on data for 6 × 6 system we conclude that sampling with sign (minus-sign problem) is probably detrimental to the accuracy of fermionic simulations with determinant algorithms.
Energy Technology Data Exchange (ETDEWEB)
Saori Pastore, S.C. Pieper, Rocco Schiavilla, Robert Wiringa
2013-03-01
Quantum Monte Carlo calculations of electromagnetic moments and transitions are reported for A{<=}9 nuclei. The realistic Argonne v{sub 18} two-nucleon and Illinois-7 three-nucleon potentials are used to generate the nuclear wave functions. Contributions of two-body meson-exchange current (MEC) operators are included for magnetic moments and M1 transitions. The MEC operators have been derived in both a standard nuclear physics approach and a chiral effective field theory formulation with pions and nucleons including up to one-loop corrections. The two-body MEC contributions provide significant corrections and lead to very good agreement with experiment. Their effect is particularly pronounced in the A=9, T=3/2 systems, in which they provide up to ~20% (~40%) of the total predicted value for the {sup 9}Li ({sup 9}C) magnetic moment.
Shepherd, James J; Scuseria, Gustavo E
2016-01-01
Over the past few years pair coupled cluster doubles (pCCD) has shown promise for the description of strong correlation. This promise is related to its apparent ability to match results from doubly occupied configuration interaction (DOCI), even though the latter method has exponential computational cost. Here, by modifying the full configuration interaction quantum Monte Carlo (FCIQMC) algorithm to sample only the seniority zero sector of Hilbert space, we show that the DOCI and pCCD energies are in agreement for a variety of 2D Hubbard models, including for systems well out of reach for conventional configuration interaction algorithms. Our calculations are aided by the sign problem being much reduced in the seniority zero space compared with the full space. We present evidence for this, and then discuss the sign problem in terms of the wave function of the system which appears to have a simplified sign structure.
Shepherd, James J.; Henderson, Thomas M.; Scuseria, Gustavo E.
2016-03-01
Over the past few years, pair coupled cluster doubles (pCCD) has shown promise for the description of strong correlation. This promise is related to its apparent ability to match results from doubly occupied configuration interaction (DOCI), even though the latter method has exponential computational cost. Here, by modifying the full configuration interaction quantum Monte Carlo algorithm to sample only the seniority zero sector of Hilbert space, we show that the DOCI and pCCD energies are in agreement for a variety of 2D Hubbard models, including for systems well out of reach for conventional configuration interaction algorithms. Our calculations are aided by the sign problem being much reduced in the seniority zero space compared with the full space. We present evidence for this and then discuss the sign problem in terms of the wave function of the system which appears to have a simplified sign structure.
Shishmarev, Dmitry; Chapman, Bogdan E; Naumann, Christoph; Mamone, Salvatore; Kuchel, Philip W
2015-01-01
The (1)H NMR signal of the methyl group of sodium acetate is shown to be a triplet in the anisotropic environment of stretched gelatin gel. The multiplet structure of the signal is due to the intra-methyl residual dipolar couplings. The relaxation properties of the spin system were probed by recording steady-state irradiation envelopes ('z-spectra'). A quantum-mechanical model based on irreducible spherical tensors formed by the three magnetically equivalent spins of the methyl group was used to simulate and fit experimental z-spectra. The multiple parameter values of the relaxation model were estimated by using a Bayesian-based Markov chain Monte Carlo algorithm. PMID:25486634
Energy Technology Data Exchange (ETDEWEB)
Teymurazyan, A. [Imaging Research, Sunnybrook Health Sciences Centre, Department of Medical Biophysics, University of Toronto, Toronto M4N 3M5 (Canada); Rowlands, J. A. [Imaging Research, Sunnybrook Health Sciences Centre, Department of Medical Biophysics, University of Toronto, Toronto M4N 3M5 (Canada); Thunder Bay Regional Research Institute (TBRRI), Thunder Bay P7A 7T1 (Canada); Department of Radiation Oncology, University of Toronto, Toronto M5S 3E2 (Canada); Pang, G., E-mail: geordi.pang@sunnybrook.ca [Imaging Research, Sunnybrook Health Sciences Centre, Department of Medical Biophysics, University of Toronto, Toronto M4N 3M5 (Canada); Department of Radiation Oncology, University of Toronto, Toronto M5S 3E2 (Canada); Odette Cancer Centre, Toronto M4N 3M5 (Canada); Department of Physics, Ryerson University, Toronto M5B 2K3 (Canada)
2014-04-15
Purpose: Electronic Portal Imaging Devices (EPIDs) have been widely used in radiation therapy and are still needed on linear accelerators (Linacs) equipped with kilovoltage cone beam CT (kV-CBCT) or MRI systems. Our aim is to develop a new high quantum efficiency (QE) Čerenkov Portal Imaging Device (CPID) that is quantum noise limited at dose levels corresponding to a single Linac pulse. Methods: Recently a new concept of CPID for MV x-ray imaging in radiation therapy was introduced. It relies on Čerenkov effect for x-ray detection. The proposed design consisted of a matrix of optical fibers aligned with the incident x-rays and coupled to an active matrix flat panel imager (AMFPI) for image readout. A weakness of such design is that too few Čerenkov light photons reach the AMFPI for each incident x-ray and an AMFPI with an avalanche gain is required in order to overcome the readout noise for portal imaging application. In this work the authors propose to replace the optical fibers in the CPID with light guides without a cladding layer that are suspended in air. The air between the light guides takes on the role of the cladding layer found in a regular optical fiber. Since air has a significantly lower refractive index (∼1 versus 1.38 in a typical cladding layer), a much superior light collection efficiency is achieved. Results: A Monte Carlo simulation of the new design has been conducted to investigate its feasibility. Detector quantities such as quantum efficiency (QE), spatial resolution (MTF), and frequency dependent detective quantum efficiency (DQE) have been evaluated. The detector signal and the quantum noise have been compared to the readout noise. Conclusions: Our studies show that the modified new CPID has a QE and DQE more than an order of magnitude greater than that of current clinical systems and yet a spatial resolution similar to that of current low-QE flat-panel based EPIDs. Furthermore it was demonstrated that the new CPID does not require an
Directory of Open Access Journals (Sweden)
Ambrish Singh
2015-08-01
Full Text Available The inhibition of the corrosion of N80 steel in 3.5 wt. % NaCl solution saturated with CO2 by four porphyrins, namely 5,10,15,20-tetrakis(4-hydroxyphenyl-21H,23H-porphyrin (HPTB, 5,10,15,20-tetra(4-pyridyl-21H,23H-porphyrin (T4PP, 4,4′,4″,4‴-(porphyrin-5,10,15,20-tetrayltetrakis(benzoic acid (THP and 5,10,15,20-tetraphenyl-21H,23H-porphyrin (TPP was studied using electrochemical impedance spectroscopy (EIS, potentiodynamic polarization, scanning electrochemical microscopy (SECM and scanning electron microscopy (SEM techniques. The results showed that the inhibition efficiency, η% increases with increasing concentration of the inhibitors. The EIS results revealed that the N80 steel surface with adsorbed porphyrins exhibited non-ideal capacitive behaviour with reduced charge transfer activity. Potentiodynamic polarization measurements indicated that the studied porphyrins acted as mixed type inhibitors. The SECM results confirmed the adsorption of the porphyrins on N80 steel thereby forming a relatively insulated surface. The SEM also confirmed the formation of protective films of the porphyrins on N80 steel surface thereby protecting the surface from direct acid attack. Quantum chemical calculations, quantitative structure activity relationship (QSAR were also carried out on the studied porphyrins and the results showed that the corrosion inhibition performances of the porphyrins could be related to their EHOMO, ELUMO, ω, and μ values. Monte Carlo simulation studies showed that THP has the highest adsorption energy, while T4PP has the least adsorption energy in agreement with the values of σ from quantum chemical calculations.
Singh, Ambrish; Lin, Yuanhua; Quraishi, Mumtaz A; Olasunkanmi, Lukman O; Fayemi, Omolola E; Sasikumar, Yesudass; Ramaganthan, Baskar; Bahadur, Indra; Obot, Ime B; Adekunle, Abolanle S; Kabanda, Mwadham M; Ebenso, Eno E
2015-01-01
The inhibition of the corrosion of N80 steel in 3.5 wt. % NaCl solution saturated with CO2 by four porphyrins, namely 5,10,15,20-tetrakis(4-hydroxyphenyl)-21H,23H-porphyrin (HPTB), 5,10,15,20-tetra(4-pyridyl)-21H,23H-porphyrin (T4PP), 4,4',4″,4‴-(porphyrin-5,10,15,20-tetrayl)tetrakis(benzoic acid) (THP) and 5,10,15,20-tetraphenyl-21H,23H-porphyrin (TPP) was studied using electrochemical impedance spectroscopy (EIS), potentiodynamic polarization, scanning electrochemical microscopy (SECM) and scanning electron microscopy (SEM) techniques. The results showed that the inhibition efficiency, η% increases with increasing concentration of the inhibitors. The EIS results revealed that the N80 steel surface with adsorbed porphyrins exhibited non-ideal capacitive behaviour with reduced charge transfer activity. Potentiodynamic polarization measurements indicated that the studied porphyrins acted as mixed type inhibitors. The SECM results confirmed the adsorption of the porphyrins on N80 steel thereby forming a relatively insulated surface. The SEM also confirmed the formation of protective films of the porphyrins on N80 steel surface thereby protecting the surface from direct acid attack. Quantum chemical calculations, quantitative structure activity relationship (QSAR) were also carried out on the studied porphyrins and the results showed that the corrosion inhibition performances of the porphyrins could be related to their EHOMO, ELUMO, ω, and μ values. Monte Carlo simulation studies showed that THP has the highest adsorption energy, while T4PP has the least adsorption energy in agreement with the values of σ from quantum chemical calculations. PMID:26295223
International Nuclear Information System (INIS)
Grand canonical Monte Carlo (GCMC) simulation combined with ab initio quantum mechanics calculations were employed to study methane storage in homogeneous armchair open-ended single-walled silicon nanotubes (SWSiNTs), single-walled carbon nanotubes (SWCNTs), and single-walled silicon carbide nanotubes (SWSiCNTs) in triangular arrays. Two different groups of nanotubes were studied: the first were (12,12) SiNTs, (19,19) CNTs, and (15,15) SiCNTs and the second were (7,7) SiNTs, (11,11) CNTs, and (9,9) SiCNTs with the diameters of 26 and 15 Å for the first and second groups, respectively. The simulations were carried out at different thermodynamic states. The potential energy functions were calculated using ab initio quantum mechanics and then fitted with (12,6) Lennard–Jones potential model as a bridge between first-principles calculations and GCMC simulations. The absolute, excess, and delivery adsorption isotherms of methane were calculated for two groups of nanotubes. The specific surface area and the isosteric heat of adsorption were computed. The radial distribution functions for the adsorbed molecules on different nanotubes were also calculated. Different isotherm models were fitted with the simulation adsorption data. According to the results, the excess uptake value of methane adsorption in (11,11) CNT array exceeded the US Department of Energy target (180 V/V at 298 K and 35 bar). The results also indicate that SiNTs and SiCNTs are not desirable materials compared with corresponding CNTs for natural gas storage.
Energy Technology Data Exchange (ETDEWEB)
Mahdizadeh, Sayyed Jalil, E-mail: saja.mahdizadeh@gmail.com; Goharshadi, Elaheh K. [Ferdowsi University of Mashhad, Department of Chemistry (Iran, Islamic Republic of)
2013-01-15
Grand canonical Monte Carlo (GCMC) simulation combined with ab initio quantum mechanics calculations were employed to study methane storage in homogeneous armchair open-ended single-walled silicon nanotubes (SWSiNTs), single-walled carbon nanotubes (SWCNTs), and single-walled silicon carbide nanotubes (SWSiCNTs) in triangular arrays. Two different groups of nanotubes were studied: the first were (12,12) SiNTs, (19,19) CNTs, and (15,15) SiCNTs and the second were (7,7) SiNTs, (11,11) CNTs, and (9,9) SiCNTs with the diameters of 26 and 15 A for the first and second groups, respectively. The simulations were carried out at different thermodynamic states. The potential energy functions were calculated using ab initio quantum mechanics and then fitted with (12,6) Lennard-Jones potential model as a bridge between first-principles calculations and GCMC simulations. The absolute, excess, and delivery adsorption isotherms of methane were calculated for two groups of nanotubes. The specific surface area and the isosteric heat of adsorption were computed. The radial distribution functions for the adsorbed molecules on different nanotubes were also calculated. Different isotherm models were fitted with the simulation adsorption data. According to the results, the excess uptake value of methane adsorption in (11,11) CNT array exceeded the US Department of Energy target (180 V/V at 298 K and 35 bar). The results also indicate that SiNTs and SiCNTs are not desirable materials compared with corresponding CNTs for natural gas storage.
Caffarel, Michel; Giner, Emmanuel; Scemama, Anthony
2016-01-01
All-electron Fixed-node Diffusion Monte Carlo (FN-DMC) calculations for the nonrelativistic ground-state energy of the water molecule at equilibrium geometry are presented. The determinantal part of the trial wavefunction is obtained from a perturbatively selected Configuration Interaction calculation (CIPSI method) including up to about 1.4 million of determinants. Calculations are made using the cc-pCV$n$Z family of basis sets, with $n$=2 to 5. In contrast with most QMC works no re-optimization of the determinantal part in presence of a Jastrow is performed. For the largest cc-pCV5Z basis set the lowest upper bound for the ground-state energy reported so far of -76.43744(18) is obtained. The fixed-node energy is found to decrease regularly as a function of the cardinal number $n$ and the Complete Basis Set limit (CBS) associated with {\\it exact nodes} is easily extracted. The resulting energy of -76.43894(12) -in perfect agreement with the best experimentally derived value- is the most accurate theoretical ...
Coccia, Emanuele; Guidoni, Leonardo
2014-01-01
In this letter we report the singlet ground state structure of the full carotenoid peridinin by means of variational Monte Carlo (VMC) calculations. The VMC relaxed geometry has an average bond length alternation of 0.1165(10) {\\AA}, larger than the values obtained by DFT (PBE, B3LYP and CAM-B3LYP) and shorter than that calculated at the Hartree-Fock (HF) level. TDDFT and EOM-CCSD calculations on a reduced peridinin model confirm the HOMO-LUMO major contribution of the Bu+-like (S2) bright excited state. Many Body Green's Function Theory (MBGFT) calculations of the vertical excitation energy of the Bu+-like state for the VMC structure (VMC/MBGFT) provide excitation energy of 2.62 eV, in agreement with experimental results in n-hexane (2.72 eV). The dependence of the excitation energy on the bond length alternation in the MBGFT and TDDFT calculations with different functionals is discussed.
Melton, Cody A
2016-01-01
We compare the fixed-phase approximation with the better known, but closely related fixed-node approximation on several testing examples. We found that both approximations behave very similarly with the fixed-phase results being very close to the fixed-node method whenever nodes/phase were of high and comparable accuracy. The fixed-phase exhibited larger biases when the trial wave functions errors in the nodes/phase were intentionally driven to unrealistically large values. We also present a formalism that enables to describe wave functions with the full antisymmetry in spin-spatial degrees of freedom using our recently developed method for systems with spins as fully quantum variables. This opens new possibilities for simulations of fermionic systems in the fixed-phase approximation formalism.
Marsusi, F; Drummond, N D
2011-01-01
We have computed the absorption and emission energies and hence Stokes shifts of small diamondoids as a function of size using different theoretical approaches, including density functional theory and quantum Monte Carlo (QMC) calculations. The absorption spectra of these molecules were also investigated by time-dependent density functional theory (TD-DFT) and compared with experiment. We have analyzed the structural distortion and formation of a self-trapped exciton in the excited state, and we have studied the effects of these on the Stokes shift as a function of size. Compared to recent experiments, QMC overestimates the excitation energies by about 0.8(1) eV on average. Benefiting from a cancellation of errors, the optical gaps obtained in DFT calculations with the B3LYP functional are in better agreement with experiment. It is also shown that TD-B3LYP calculations can reproduce most of the features found in the experimental spectra. According to our calculations, the structures of diamondoids in the exci...
Energy Technology Data Exchange (ETDEWEB)
Pastore, S. [University of South Carolina; Wiringa, Robert B. [ANL; Pieper, Steven C. [ANL; Schiavilla, Rocco [Old Dominion U., JLAB
2014-08-01
We report quantum Monte Carlo calculations of electromagnetic transitions in $^8$Be. The realistic Argonne $v_{18}$ two-nucleon and Illinois-7 three-nucleon potentials are used to generate the ground state and nine excited states, with energies that are in excellent agreement with experiment. A dozen $M1$ and eight $E2$ transition matrix elements between these states are then evaluated. The $E2$ matrix elements are computed only in impulse approximation, with those transitions from broad resonant states requiring special treatment. The $M1$ matrix elements include two-body meson-exchange currents derived from chiral effective field theory, which typically contribute 20--30\\% of the total expectation value. Many of the transitions are between isospin-mixed states; the calculations are performed for isospin-pure states and then combined with the empirical mixing coefficients to compare to experiment. In general, we find that transitions between states that have the same dominant spatial symmetry are in decent agreement with experiment, but those transitions between different spatial symmetries are often significantly underpredicted.
Institute of Scientific and Technical Information of China (English)
Kong Ling-Gang; Liu Xiao-Yan; Du Gang; Wang Yi; Kang Jin-Feng; Han Ru-Qi
2006-01-01
We develop a Monte Carlo (MC) tool incorporated with the three-subband approximation model to investigate the inplane spin-polarized transport in GaAs/GaAlAs quantum well. Using the tool, the effects of the electron occupation of higher subbands and the intersubband scattering on the spin dephasing have been studied. Compared with the corresponding results of the simple one-subband approximation model, the spin dephasing length is reduced four times under 0.125kV/cm of driving electric field at 300K by the MC tool incorporated with the three-subband approximation model, indicating that the three-subband approximation model predicts significantly shorter spin dephasing length with temperature increasing. Our simulation results suggest that the effects of the electron occupation of higher subbands and the intersubband scattering on the spin-dependent transport of GaAs 2-dimensional electron gas need to be considered when the driving electric field exceeds the moderate value and the lattice temperature is above 100K. The simulation by using the MC tool incorporated with the three-subband approximation model also indicates that, under a certain driving electric field and lattice temperature, larger channel widths cause spins to be depolarized faster. Ranges of the three components of the spins are different for three different injected spin polarizations due to the anisotropy of spin orbit interaction.
Adriano Junior, L; Fonseca, T L; Castro, M A
2016-06-21
Theoretical results for the absorption spectrum and electric properties of the enol and keto tautomeric forms of anil derivatives in the gas-phase and in solution are presented. The electronic properties in chloroform, acetonitrile, methanol, and water were determined by carrying out sequential Monte Carlo simulations and quantum mechanics calculations based on the time dependent density functional theory and on the second-order Møller-Plesset perturbation theory method. The results illustrate the role played by electrostatic interactions in the electronic properties of anil derivatives in a liquid environment. There is a significant increase of the dipole moment in solution (20%-100%) relative to the gas-phase value. Solvent effects are mild for the absorption spectrum and linear polarizability but they can be particularly important for first hyperpolarizability. A large first hyperpolarizability contrast between the enol and keto forms is observed when absorption spectra present intense lowest-energy absorption bands. Dynamic results for the first hyperpolarizability are in qualitative agreement with the available experimental results. PMID:27334183
Solution to sign problems in models of interacting fermions and quantum spins
Huffman, Emilie
2016-01-01
We show that solutions to fermion sign problems in the CT-INT formulation can be extended to systems involving fermions interacting with dynamical quantum spins. While these sign problems seem unsolvable in the auxiliary field approach, solutions emerge in the worldline representation of quantum spins. Combining the idea with meron-cluster methods, we are able to extend the solvable models even further. We demonstrate these novel solutions to sign problems by considering several examples of strongly correlated systems.
International Nuclear Information System (INIS)
The present state of modeling radio-induced effects at the cellular level does not account for the microscopic inhomogeneity of the nucleus from the non-aqueous contents (i.e. proteins, DNA) by approximating the entire cellular nucleus as a homogenous medium of water. Charged particle track-structure calculations utilizing this approximation are therefore neglecting to account for approximately 30% of the molecular variation within the nucleus. To truly understand what happens when biological matter is irradiated, charged particle track-structure calculations need detailed knowledge of the secondary electron cascade, resulting from interactions with not only the primary biological component—water-–but also the non-aqueous contents, down to very low energies. This paper presents our work on a generic approach for calculating low-energy interaction cross-sections between incident charged particles and individual molecules. The purpose of our work is to develop a self-consistent computational method for predicting molecule-specific interaction cross-sections, such as the component molecules of DNA and proteins (i.e. nucleotides and amino acids), in the very low-energy regime. These results would then be applied in a track-structure code and thereby reduce the homogenous water approximation. The present methodology—inspired by seeking a combination of the accuracy of quantum mechanics and the scalability, robustness, and flexibility of Monte Carlo methods—begins with the calculation of a solution to the many-body Schrödinger equation and proceeds to use Monte Carlo methods to calculate the perturbations in the internal electron field to determine the interaction processes, such as ionization and excitation. As a test of our model, the approach is applied to a water molecule in the same method as it would be applied to a nucleotide or amino acid and compared with the low-energy cross-sections from the GEANT4-DNA physics package of the Geant4 simulation toolkit
Madsen, J. R.; Akabani, G.
2014-05-01
The present state of modeling radio-induced effects at the cellular level does not account for the microscopic inhomogeneity of the nucleus from the non-aqueous contents (i.e. proteins, DNA) by approximating the entire cellular nucleus as a homogenous medium of water. Charged particle track-structure calculations utilizing this approximation are therefore neglecting to account for approximately 30% of the molecular variation within the nucleus. To truly understand what happens when biological matter is irradiated, charged particle track-structure calculations need detailed knowledge of the secondary electron cascade, resulting from interactions with not only the primary biological component—water--but also the non-aqueous contents, down to very low energies. This paper presents our work on a generic approach for calculating low-energy interaction cross-sections between incident charged particles and individual molecules. The purpose of our work is to develop a self-consistent computational method for predicting molecule-specific interaction cross-sections, such as the component molecules of DNA and proteins (i.e. nucleotides and amino acids), in the very low-energy regime. These results would then be applied in a track-structure code and thereby reduce the homogenous water approximation. The present methodology—inspired by seeking a combination of the accuracy of quantum mechanics and the scalability, robustness, and flexibility of Monte Carlo methods—begins with the calculation of a solution to the many-body Schrödinger equation and proceeds to use Monte Carlo methods to calculate the perturbations in the internal electron field to determine the interaction processes, such as ionization and excitation. As a test of our model, the approach is applied to a water molecule in the same method as it would be applied to a nucleotide or amino acid and compared with the low-energy cross-sections from the GEANT4-DNA physics package of the Geant4 simulation toolkit
Energy Technology Data Exchange (ETDEWEB)
Dupuy, Nicolas, E-mail: nicolas.dupuy@impmc.upmc.fr [Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Université Pierre et Marie Curie, case 115, 4 place Jussieu, 75252 Paris Cedex 05 (France); Bouaouli, Samira, E-mail: samira.bouaouli@lct.jussieu.fr [Laboratoire de Chimie Théorique, Université Pierre et Marie Curie, case 115, 4 place Jussieu, 75252 Paris Cedex 05 (France); Mauri, Francesco, E-mail: francesco.mauri@impmc.upmc.fr; Casula, Michele, E-mail: michele.casula@impmc.upmc.fr [CNRS and Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Université Pierre et Marie Curie, case 115, 4 place Jussieu, 75252 Paris Cedex 05 (France); Sorella, Sandro, E-mail: sorella@sissa.it [International School for Advanced Studies (SISSA), Via Beirut 2-4, 34014 Trieste, Italy and INFM Democritos National Simulation Center, Trieste (Italy)
2015-06-07
We study the ionization energy, electron affinity, and the π → π{sup ∗} ({sup 1}L{sub a}) excitation energy of the anthracene molecule, by means of variational quantum Monte Carlo (QMC) methods based on a Jastrow correlated antisymmetrized geminal power (JAGP) wave function, developed on molecular orbitals (MOs). The MO-based JAGP ansatz allows one to rigorously treat electron transitions, such as the HOMO → LUMO one, which underlies the {sup 1}L{sub a} excited state. We present a QMC optimization scheme able to preserve the rank of the antisymmetrized geminal power matrix, thanks to a constrained minimization with projectors built upon symmetry selected MOs. We show that this approach leads to stable energy minimization and geometry relaxation of both ground and excited states, performed consistently within the correlated QMC framework. Geometry optimization of excited states is needed to make a reliable and direct comparison with experimental adiabatic excitation energies. This is particularly important in π-conjugated and polycyclic aromatic hydrocarbons, where there is a strong interplay between low-lying energy excitations and structural modifications, playing a functional role in many photochemical processes. Anthracene is an ideal benchmark to test these effects. Its geometry relaxation energies upon electron excitation are of up to 0.3 eV in the neutral {sup 1}L{sub a} excited state, while they are of the order of 0.1 eV in electron addition and removal processes. Significant modifications of the ground state bond length alternation are revealed in the QMC excited state geometry optimizations. Our QMC study yields benchmark results for both geometries and energies, with values below chemical accuracy if compared to experiments, once zero point energy effects are taken into account.
Dupuy, Nicolas; Bouaouli, Samira; Mauri, Francesco; Sorella, Sandro; Casula, Michele
2015-06-01
We study the ionization energy, electron affinity, and the π → π(∗) ((1)La) excitation energy of the anthracene molecule, by means of variational quantum Monte Carlo (QMC) methods based on a Jastrow correlated antisymmetrized geminal power (JAGP) wave function, developed on molecular orbitals (MOs). The MO-based JAGP ansatz allows one to rigorously treat electron transitions, such as the HOMO → LUMO one, which underlies the (1)La excited state. We present a QMC optimization scheme able to preserve the rank of the antisymmetrized geminal power matrix, thanks to a constrained minimization with projectors built upon symmetry selected MOs. We show that this approach leads to stable energy minimization and geometry relaxation of both ground and excited states, performed consistently within the correlated QMC framework. Geometry optimization of excited states is needed to make a reliable and direct comparison with experimental adiabatic excitation energies. This is particularly important in π-conjugated and polycyclic aromatic hydrocarbons, where there is a strong interplay between low-lying energy excitations and structural modifications, playing a functional role in many photochemical processes. Anthracene is an ideal benchmark to test these effects. Its geometry relaxation energies upon electron excitation are of up to 0.3 eV in the neutral (1)La excited state, while they are of the order of 0.1 eV in electron addition and removal processes. Significant modifications of the ground state bond length alternation are revealed in the QMC excited state geometry optimizations. Our QMC study yields benchmark results for both geometries and energies, with values below chemical accuracy if compared to experiments, once zero point energy effects are taken into account. PMID:26049481
International Nuclear Information System (INIS)
We study the ionization energy, electron affinity, and the π → π∗ (1La) excitation energy of the anthracene molecule, by means of variational quantum Monte Carlo (QMC) methods based on a Jastrow correlated antisymmetrized geminal power (JAGP) wave function, developed on molecular orbitals (MOs). The MO-based JAGP ansatz allows one to rigorously treat electron transitions, such as the HOMO → LUMO one, which underlies the 1La excited state. We present a QMC optimization scheme able to preserve the rank of the antisymmetrized geminal power matrix, thanks to a constrained minimization with projectors built upon symmetry selected MOs. We show that this approach leads to stable energy minimization and geometry relaxation of both ground and excited states, performed consistently within the correlated QMC framework. Geometry optimization of excited states is needed to make a reliable and direct comparison with experimental adiabatic excitation energies. This is particularly important in π-conjugated and polycyclic aromatic hydrocarbons, where there is a strong interplay between low-lying energy excitations and structural modifications, playing a functional role in many photochemical processes. Anthracene is an ideal benchmark to test these effects. Its geometry relaxation energies upon electron excitation are of up to 0.3 eV in the neutral 1La excited state, while they are of the order of 0.1 eV in electron addition and removal processes. Significant modifications of the ground state bond length alternation are revealed in the QMC excited state geometry optimizations. Our QMC study yields benchmark results for both geometries and energies, with values below chemical accuracy if compared to experiments, once zero point energy effects are taken into account
Al-Khalili, Jim
2003-01-01
In this lively look at quantum science, a physicist takes you on an entertaining and enlightening journey through the basics of subatomic physics. Along the way, he examines the paradox of quantum mechanics--beautifully mathematical in theory but confoundingly unpredictable in the real world. Marvel at the Dual Slit experiment as a tiny atom passes through two separate openings at the same time. Ponder the peculiar communication of quantum particles, which can remain in touch no matter how far apart. Join the genius jewel thief as he carries out a quantum measurement on a diamond without ever touching the object in question. Baffle yourself with the bizzareness of quantum tunneling, the equivalent of traveling partway up a hill, only to disappear then reappear traveling down the opposite side. With its clean, colorful layout and conversational tone, this text will hook you into the conundrum that is quantum mechanics.
International Nuclear Information System (INIS)
We develop a formalism and present an algorithm for optimization of the trial wave-function used in fixed-node diffusion quantum Monte Carlo (DMC) methods. The formalism is based on the DMC mixed estimator of the ground state probability density. We take advantage of a basic property of the walker configuration distribution generated in a DMC calculation, to (i) project-out a multi-determinant expansion of the fixed node ground state wave function and (ii) to define a cost function that relates the interacting-ground-state-fixed-node and the non-interacting trial wave functions. We show that (a) locally smoothing out the kink of the fixed-node ground-state wave function at the node generates a new trial wave function with better nodal structure and (b) we argue that the noise in the fixed-node wave function resulting from finite sampling plays a beneficial role, allowing the nodes to adjust towards the ones of the exact many-body ground state in a simulated annealing-like process. Based on these principles, we propose a method to improve both single determinant and multi-determinant expansions of the trial wave function. The method can be generalized to other wave function forms such as pfaffians. We test the method in a model system where benchmark configuration interaction calculations can be performed and most components of the Hamiltonian are evaluated analytically. Comparing the DMC calculations with the exact solutions, we find that the trial wave function is systematically improved. The overlap of the optimized trial wave function and the exact ground state converges to 100% even starting from wave functions orthogonal to the exact ground state. Similarly, the DMC total energy and density converges to the exact solutions for the model. In the optimization process we find an optimal non-interacting nodal potential of density-functional-like form whose existence was predicted in a previous publication (Phys. Rev. B 77 245110 (2008)). Tests of the method are
Energy Technology Data Exchange (ETDEWEB)
Reboredo, F A; Hood, R Q; Kent, P C
2009-01-06
We develop a formalism and present an algorithm for optimization of the trial wave-function used in fixed-node diffusion quantum Monte Carlo (DMC) methods. The formalism is based on the DMC mixed estimator of the ground state probability density. We take advantage of a basic property of the walker configuration distribution generated in a DMC calculation, to (i) project-out a multi-determinant expansion of the fixed node ground state wave function and (ii) to define a cost function that relates the interacting-ground-state-fixed-node and the non-interacting trial wave functions. We show that (a) locally smoothing out the kink of the fixed-node ground-state wave function at the node generates a new trial wave function with better nodal structure and (b) we argue that the noise in the fixed-node wave function resulting from finite sampling plays a beneficial role, allowing the nodes to adjust towards the ones of the exact many-body ground state in a simulated annealing-like process. Based on these principles, we propose a method to improve both single determinant and multi-determinant expansions of the trial wave function. The method can be generalized to other wave function forms such as pfaffians. We test the method in a model system where benchmark configuration interaction calculations can be performed and most components of the Hamiltonian are evaluated analytically. Comparing the DMC calculations with the exact solutions, we find that the trial wave function is systematically improved. The overlap of the optimized trial wave function and the exact ground state converges to 100% even starting from wave functions orthogonal to the exact ground state. Similarly, the DMC total energy and density converges to the exact solutions for the model. In the optimization process we find an optimal non-interacting nodal potential of density-functional-like form whose existence was predicted in a previous publication [Phys. Rev. B 77 245110 (2008)]. Tests of the method are
Mean field simulation for Monte Carlo integration
Del Moral, Pierre
2013-01-01
In the last three decades, there has been a dramatic increase in the use of interacting particle methods as a powerful tool in real-world applications of Monte Carlo simulation in computational physics, population biology, computer sciences, and statistical machine learning. Ideally suited to parallel and distributed computation, these advanced particle algorithms include nonlinear interacting jump diffusions; quantum, diffusion, and resampled Monte Carlo methods; Feynman-Kac particle models; genetic and evolutionary algorithms; sequential Monte Carlo methods; adaptive and interacting Marko
A Quantum Monte Carlo Study on Mixed-Spin Chains of 1／2-1／2-1-1 and 3／2-3／2-1-1
Institute of Scientific and Technical Information of China (English)
XUZhao-Xin; ZHANGJun; YINGHe-Ping
2003-01-01
The ground-state and thermodynamic properties of quantum mixed-spin chains of 1/2-1/2-1-1 and 3/2-3/2-1-1 are investigated by a quantum Monte Carlo simulation with the loop-cluster algorithm. For 1/2-1/2-1-1 chain, we find it hastwo phases separated by an energy-gap vanishing point in the ground-state. For 3/2-3/2-1-1 chain,the numerical results show two energy-gap vanishing points isolated by different phases in its ground-state. Our calculations indicate that all these ground state phases can be understood by means of valence-bond-solid picture, and the thermodynamic behavior at finite temperatures is continuous as a function of parameter α=J2/J1.
Caffarel, Michel; Scemama, Anthony; Ramírez-Solís, Alejandro
2014-01-01
We present a comparative study of the spatial distribution of the spin density (SD) of the ground state of CuCl2 using Density Functional Theory (DFT), quantum Monte Carlo (QMC), and post-Hartree-Fock wavefunction theory (WFT). A number of studies have shown that an accurate description of the electronic structure of the lowest-lying states of this molecule is particularly challenging due to the interplay between the strong dynamical correlation effects in the 3d shell of the copper atom and the delocalization of the 3d hole over the chlorine atoms. It is shown here that qualitatively different results for SD are obtained from these various quantum-chemical approaches. At the DFT level, the spin density distribution is directly related to the amount of Hartree-Fock exchange introduced in hybrid functionals. At the QMC level, Fixed-node Diffusion Monte Carlo (FN-DMC) results for SD are strongly dependent on the nodal structure of the trial wavefunction employed (here, Hartree-Fock or Kohn-Sham with a particula...
Kritsotakis, M.; Kominis, I. K.
2014-01-01
Radical-ion-pair reactions, central in photosynthesis and the avian magnetic compass mechanism, have recently shown to be a paradigm system for applying quantum information science in a biochemical setting. The fundamental quantum master equation describing radical-ion-pair reactions is still under debate. We here use quantum retrodiction to produce a rigorous refinement of the theory put forward in Phys. Rev. E {\\bf 83}, 056118 (2011). We also provide a rigorous analysis of the measure of si...
Computing quantum phase transitions
Vojta, Thomas
2007-01-01
This article first gives a concise introduction to quantum phase transitions, emphasizing similarities with and differences to classical thermal transitions. After pointing out the computational challenges posed by quantum phase transitions, a number of successful computational approaches is discussed. The focus is on classical and quantum Monte Carlo methods, with the former being based on the quantum-to classical mapping while the latter directly attack the quantum problem. These methods ar...
Resummed perturbative series of scalar quantum field theories in two-particle-irreducible formalism
Fejos, G
2011-01-01
In this thesis the two-particle-irreducible (2PI) formalism is investigated with several applications, particular emphasis on renormalizability. In the O(N) symmetric scalar quantum field theory formulated with auxiliary fields it is pointed out that, statements recently appeared in the literature which raised doubts on renormalizability, are wrong. Counterterms are constructed in details in the NLO of the large-N expansion. The renormalizability is demonstrated at the same level of the approximation also with eliminating the auxiliary field. In the one component \\phi^4 model (at T=0) a method using renormalization conditions is developed, which gives directly finite equations for the 1- and 2-point functions. This solves the problems of numerical precision of the counterterm formulated renormalization. In the two-loop 2PI approximation the equivalence of the new method and the procedure formulated with counterterms is shown, both analytically and numerically. For the counterterm method also a new algorithm i...
Quantum Monte Carlo Computations of the (Mg1-XFeX) SiO3 Perovskite to Post-perovskite Phase Boundary
Lin, Yangzheng; Cohen, R. E.; Floris, Andrea; Shulenburger, Luke; Driver, Kevin P.
We have computed total energies of FeSiO3 and MgSiO3[1 ] perovskite and post-perovskite using diffusion Monte Carlo with the qmcpack GPU code. In conjunction with DFT +U computations for intermediate compositions (Mg1-XFeX) SiO3 and phonons computed using density functional perturbation theory (DFPT) with the pwscf code, we have derived the chemical potentials of perovskite (Pv) and post-perovskite (PPv) (Mg1-XFeX) SiO3 and computed the binary phase diagram versus P, T, and X using a non-ideal solid solution model. The finite temperature effects were considered within quasi-harmonic approximation (QHA). Our results show that ferrous iron stabilizes PPv and lowers the Pv-PPv transition pressure, which is consistent with previous theoretical and some experimental studies. We will discuss the correlation between the Earth's D'' layer and the Pv to PPv phase boundary. Computations were performed on XSEDE machines, and on the Oak Ridge Leadership Computing Facility (OLCF) machine Titan under project CPH103geo of INCITE program E-mail: rcohen@carnegiescience.edu; This work is supported by NSF.
Schachenmayer, J.; Pikovski, A.; Rey, A. M.
2015-06-01
Interacting quantum spin models are remarkably useful for describing different types of physical, chemical, and biological systems. Significant understanding of their equilibrium properties has been achieved to date, especially for the case of spin models with short-range couplings. However, progress toward the development of a comparable understanding in long-range interacting models, in particular out-of-equilibrium, remains limited. In a recent work, we proposed a semiclassical numerical method to study spin models, the discrete truncated Wigner approximation (DTWA), and demonstrated its capability to correctly capture the dynamics of one- and two-point correlations in one-dimensional (1D) systems. Here we go one step forward and use the DTWA method to study the dynamics of correlations in two-dimensional (2D) systems with many spins and different types of long-range couplings, in regimes where other numerical methods are generally unreliable. We compute spatial and time-dependent correlations for spin-couplings that decay with distance as a power-law and determine the velocity at which correlations propagate through the system. Sharp changes in the behavior of those velocities are found as a function of the power-law decay exponent. Our predictions are relevant for a broad range of systems including solid state materials, atom-photon systems and ultracold gases of polar molecules, trapped ions, Rydberg, and magnetic atoms. We validate the DTWA predictions for small 2D systems and 1D systems, but ultimately, in the spirt of quantum simulation, experiments will be needed to confirm our predictions for large 2D systems.
Shell model Monte Carlo methods
International Nuclear Information System (INIS)
We review quantum Monte Carlo methods for dealing with large shell model problems. These methods reduce the imaginary-time many-body evolution operator to a coherent superposition of one-body evolutions in fluctuating one-body fields; resultant path integral is evaluated stochastically. We first discuss the motivation, formalism, and implementation of such Shell Model Monte Carlo methods. There then follows a sampler of results and insights obtained from a number of applications. These include the ground state and thermal properties of pf-shell nuclei, thermal behavior of γ-soft nuclei, and calculation of double beta-decay matrix elements. Finally, prospects for further progress in such calculations are discussed. 87 refs
Numerical calculations in quantum field theories
International Nuclear Information System (INIS)
Four lecture notes are included: (1) motivation for numerical calculations in Quantum Field Theory; (2) numerical simulation methods; (3) Monte Carlo studies of Quantum Chromo Dynamics; and (4) systems with fermions. 23 references
Boblest, S.; Meyer, D.; Wunner, G.
2014-11-01
We present a quantum Monte Carlo application for the computation of energy eigenvalues for atoms and ions in strong magnetic fields. The required guiding wave functions are obtained with the Hartree-Fock-Roothaan code described in the accompanying publication (Schimeczek and Wunner, 2014). Our method yields highly accurate results for the binding energies of symmetry subspace ground states and at the same time provides a means for quantifying the quality of the results obtained with the above-mentioned Hartree-Fock-Roothaan method. Catalogue identifier: AETV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AETV_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 72 284 No. of bytes in distributed program, including test data, etc.: 604 948 Distribution format: tar.gz Programming language: C++. Computer: Cluster of 1-˜500 HP Compaq dc5750. Operating system: Linux. Has the code been vectorized or parallelized?: Yes. Code includes MPI directives. RAM: 500 MB per node Classification: 2.1. External routines: Boost::Serialization, Boost::MPI, LAPACK BLAS Nature of problem: Quantitative modelings of features observed in the X-ray spectra of isolated neutron stars are hampered by the lack of sufficiently large and accurate databases for atoms and ions up to the last fusion product iron, at high magnetic field strengths. The predominant amount of line data in the literature has been calculated with Hartree-Fock methods, which are intrinsically restricted in precision. Our code is intended to provide a powerful tool for calculating very accurate energy values from, and thereby improving the quality of, existing Hartree-Fock results. Solution method: The Fixed-phase quantum Monte Carlo method is used in combination with guiding functions obtained in Hartree
Controlling Quantum Information
Landahl, A J
2002-01-01
Quantum information science explores ways in which quantum physical laws can be harnessed to control the acquisition, transmission, protection, and processing of information. This field has seen explosive growth in the past several years from progress on both theoretical and experimental fronts. Essential to this endeavor are methods for controlling quantum information. In this thesis, I present three new approaches for controlling quantum information. First, I present a new protocol for continuously protecting unknown quantum states from noise. This protocol combines and expands ideas from the theories of quantum error correction and quantum feedback control. The result can outperform either approach by itself. I generalize this protocol to all known quantum stabilizer codes, and study its application to the three-qubit repetition code in detail via Monte Carlo simulations. Next, I present several new protocols for controlling quantum information that are fault-tolerant. These protocols require only local qu...
Yet another Monte Carlo study of the Schwinger model
International Nuclear Information System (INIS)
Some methodological improvements are introduced in the quantum Monte Carlo simulation of the 1 + 1 dimensional quantum electrodynamics (the Schwinger model). Properties at finite temperatures are investigated, concentrating on the existence of the chirality transition and of the deconfinement transition. (author)
Introduction to algorithms for Monte Carlo simulations and their application to QCD
International Nuclear Information System (INIS)
This paper contains an introduction to Monte Carlo simulations for systems defined by their probability to be in a given configuration. Examples of such systems are lattice models in statistical mechanics and quantum field theories in Euclidean time. The emphasis is on the algorithms used in simulating quantum chromodynamics (QCD). The fermion problem for quantum field theories is described, and then the application of Monte Carlo simulation to QCD is briefly described. (orig.)
Thermal, quantum and simulated quantum annealing: analytical comparisons for simple models
Bapst, Victor; Semerjian, Guilhem
2015-01-01
We study various annealing dynamics, both classical and quantum, for simple mean-field models and explain how to describe their behavior in the thermodynamic limit in terms of differential equations. In particular we emphasize the differences between quantum annealing (i.e. evolution with Schr\\"odinger equation) and simulated quantum annealing (i.e. annealing of a Quantum Monte Carlo simulation).
Monte Carlo study of real time dynamics
Alexandru, Andrei; Bedaque, Paulo F; Vartak, Sohan; Warrington, Neill C
2016-01-01
Monte Carlo studies involving real time dynamics are severely restricted by the sign problem that emerges from highly oscillatory phase of the path integral. In this letter, we present a new method to compute real time quantities on the lattice using the Schwinger-Keldysh formalism via Monte Carlo simulations. The key idea is to deform the path integration domain to a complex manifold where the phase oscillations are mild and the sign problem is manageable. We use the previously introduced "contraction algorithm" to create a Markov chain on this alternative manifold. We substantiate our approach by analyzing the quantum mechanical anharmonic oscillator. Our results are in agreement with the exact ones obtained by diagonalization of the Hamiltonian. The method we introduce is generic and in principle applicable to quantum field theory albeit very slow. We discuss some possible improvements that should speed up the algorithm.
Dunn, William L
2012-01-01
Exploring Monte Carlo Methods is a basic text that describes the numerical methods that have come to be known as "Monte Carlo." The book treats the subject generically through the first eight chapters and, thus, should be of use to anyone who wants to learn to use Monte Carlo. The next two chapters focus on applications in nuclear engineering, which are illustrative of uses in other fields. Five appendices are included, which provide useful information on probability distributions, general-purpose Monte Carlo codes for radiation transport, and other matters. The famous "Buffon's needle proble
Archimedes, the Free Monte Carlo simulator
Sellier, Jean Michel D.
2012-01-01
Archimedes is the GNU package for Monte Carlo simulations of electron transport in semiconductor devices. The first release appeared in 2004 and since then it has been improved with many new features like quantum corrections, magnetic fields, new materials, GUI, etc. This document represents the first attempt to have a complete manual. Many of the Physics models implemented are described and a detailed description is presented to make the user able to write his/her own input deck. Please, fee...
Monte Carlo methods and applications in nuclear physics
International Nuclear Information System (INIS)
Monte Carlo methods for studying few- and many-body quantum systems are introduced, with special emphasis given to their applications in nuclear physics. Variational and Green's function Monte Carlo methods are presented in some detail. The status of calculations of light nuclei is reviewed, including discussions of the three-nucleon-interaction, charge and magnetic form factors, the coulomb sum rule, and studies of low-energy radiative transitions. 58 refs., 12 figs
Abrams, Daniel S.
This thesis describes several new quantum algorithms. These include a polynomial time algorithm that uses a quantum fast Fourier transform to find eigenvalues and eigenvectors of a Hamiltonian operator, and that can be applied in cases (commonly found in ab initio physics and chemistry problems) for which all known classical algorithms require exponential time. Fast algorithms for simulating many body Fermi systems are also provided in both first and second quantized descriptions. An efficient quantum algorithm for anti-symmetrization is given as well as a detailed discussion of a simulation of the Hubbard model. In addition, quantum algorithms that calculate numerical integrals and various characteristics of stochastic processes are described. Two techniques are given, both of which obtain an exponential speed increase in comparison to the fastest known classical deterministic algorithms and a quadratic speed increase in comparison to classical Monte Carlo (probabilistic) methods. I derive a simpler and slightly faster version of Grover's mean algorithm, show how to apply quantum counting to the problem, develop some variations of these algorithms, and show how both (apparently distinct) approaches can be understood from the same unified framework. Finally, the relationship between physics and computation is explored in some more depth, and it is shown that computational complexity theory depends very sensitively on physical laws. In particular, it is shown that nonlinear quantum mechanics allows for the polynomial time solution of NP-complete and #P oracle problems. Using the Weinberg model as a simple example, the explicit construction of the necessary gates is derived from the underlying physics. Nonlinear quantum algorithms are also presented using Polchinski type nonlinearities which do not allow for superluminal communication. (Copies available exclusively from MIT Libraries, Rm. 14- 0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)
One- and two-particle correlation functions in the dynamical quantum cluster approach
Energy Technology Data Exchange (ETDEWEB)
Hochkeppel, Stephan
2008-07-25
This thesis is dedicated to a theoretical study of the 1-band Hubbard model in the strong coupling limit. The investigation is based on the Dynamical Cluster Approximation (DCA) which systematically restores non-local corrections to the Dynamical Mean Field approximation (DMFA). The DCA is formulated in momentum space and is characterised by a patching of the Brillouin zone where momentum conservation is only recovered between two patches. The approximation works well if k-space correlation functions show a weak momentum dependence. In order to study the temperature and doping dependence of the spin- and charge excitation spectra, we explicitly extend the Dynamical Cluster Approximation to two-particle response functions. The full irreducible two-particle vertex with three momenta and frequencies is approximated by an effective vertex dependent on the momentum and frequency of the spin and/or charge excitations. The effective vertex is calculated by using the Quantum Monte Carlo method on the finite cluster whereas the analytical continuation of dynamical quantities is performed by a stochastic version of the maximum entropy method. A comparison with high temperature auxiliary field quantum Monte Carlo data serves as a benchmark for our approach to two-particle correlation functions. Our method can reproduce basic characteristics of the spin- and charge excitation spectrum. Near and beyond optimal doping, our results provide a consistent overall picture of the interplay between charge, spin and single-particle excitations: a collective spin mode emerges at optimal doping and sufficiently low temperatures in the spin response spectrum and exhibits the energy scale of the magnetic exchange interaction J. Simultaneously, the low energy single-particle excitations are characterised by a coherent quasiparticle with bandwidth J. The origin of the quasiparticle can be quite well understood in a picture of a more or less antiferromagnetic ordered background in which holes
Quanten-Monte-Carlo : Optimierung von Wellenfunktionen und Benchmarkrechnungen
Schwarz, Annett
2011-01-01
The basic idea of the diffusion quantum Monte Carlo method (DMC) is the analogy of the Schrödinger equation in imaginary time and atomic units to a generalized diffusion equation and the numerical simulation of the diffusion according to a random walk process. DMC yields the exact statistical solution of the Schrödinger equation for boson systems. A possibility to describe fermions is the fixed-node diffusion quantum Monte Carlo method (FN-DMC). In the FN-DMC approach the nodes of the trial w...
Monte Carlo Radiative Transfer
Whitney, Barbara A
2011-01-01
I outline methods for calculating the solution of Monte Carlo Radiative Transfer (MCRT) in scattering, absorption and emission processes of dust and gas, including polarization. I provide a bibliography of relevant papers on methods with astrophysical applications.
Monte Carlo transition probabilities
Lucy, L. B.
2001-01-01
Transition probabilities governing the interaction of energy packets and matter are derived that allow Monte Carlo NLTE transfer codes to be constructed without simplifying the treatment of line formation. These probabilities are such that the Monte Carlo calculation asymptotically recovers the local emissivity of a gas in statistical equilibrium. Numerical experiments with one-point statistical equilibrium problems for Fe II and Hydrogen confirm this asymptotic behaviour. In addition, the re...
Energy Technology Data Exchange (ETDEWEB)
Wollaber, Allan Benton [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-06-16
This is a powerpoint which serves as lecture material for the Parallel Computing summer school. It goes over the fundamentals of Monte Carlo. Welcome to Los Alamos, the birthplace of “Monte Carlo” for computational physics. Stanislaw Ulam, John von Neumann, and Nicholas Metropolis are credited as the founders of modern Monte Carlo methods. The name “Monte Carlo” was chosen in reference to the Monte Carlo Casino in Monaco (purportedly a place where Ulam’s uncle went to gamble). The central idea (for us) – to use computer-generated “random” numbers to determine expected values or estimate equation solutions – has since spread to many fields. "The first thoughts and attempts I made to practice [the Monte Carlo Method] were suggested by a question which occurred to me in 1946 as I was convalescing from an illness and playing solitaires. The question was what are the chances that a Canfield solitaire laid out with 52 cards will come out successfully? After spending a lot of time trying to estimate them by pure combinatorial calculations, I wondered whether a more practical method than “abstract thinking” might not be to lay it out say one hundred times and simply observe and count the number of successful plays... Later [in 1946], I described the idea to John von Neumann, and we began to plan actual calculations." - Stanislaw Ulam.
Auxiliary fields in the geometrical relativistic particle dynamics
International Nuclear Information System (INIS)
We describe how to construct the dynamics of relativistic particles, following either timelike or null curves, by means of an auxiliary variables method instead of the standard theory of deformations for curves. There are interesting physical particle models governed by actions that involve higher order derivatives of the embedding functions of the worldline. We point out that the mechanical content of such models can be extracted wisely from a lower order action, which can be performed by implementing in the action a finite number of constraints that involve the geometrical relationship structures inherent to a curve and by using a covariant formalism. We emphasize our approach for null curves. For such systems, the natural time parameter is a pseudo-arclength whose properties resemble those of the standard proper time. We illustrate the formalism by applying it to some models for relativistic particles
Auxiliary fields in the geometrical relativistic particle dynamics
Energy Technology Data Exchange (ETDEWEB)
Amador, A; Bagatella, N; Rojas, E [Departamento de Fisica, Facultad de Fisica e Inteligencia Artificial, Universidad Veracruzana, 91000 Xalapa, Veracruz (Mexico); Cordero, R [Departamento de Fisica, Escuela Superior de Fisica y Matematicas del I.P.N, Edificio 9, 07738 Mexico D.F (Mexico)], E-mail: aramador@gmail.com, E-mail: nbagatella@uv.mx, E-mail: cordero@esfm.ipn.mx, E-mail: efrojas@uv.mx
2008-03-21
We describe how to construct the dynamics of relativistic particles, following either timelike or null curves, by means of an auxiliary variables method instead of the standard theory of deformations for curves. There are interesting physical particle models governed by actions that involve higher order derivatives of the embedding functions of the worldline. We point out that the mechanical content of such models can be extracted wisely from a lower order action, which can be performed by implementing in the action a finite number of constraints that involve the geometrical relationship structures inherent to a curve and by using a covariant formalism. We emphasize our approach for null curves. For such systems, the natural time parameter is a pseudo-arclength whose properties resemble those of the standard proper time. We illustrate the formalism by applying it to some models for relativistic particles.
Monte Carlo Shell Model Mass Predictions
International Nuclear Information System (INIS)
The nuclear mass calculation is discussed in terms of large-scale shell model calculations. First, the development and limitations of the conventional shell model calculations are mentioned. In order to overcome the limitations, the Quantum Monte Carlo Diagonalization (QMCD) method has been proposed. The basic formulation and features of the QMCD method are presented as well as its application to the nuclear shell model, referred to as Monte Carlo Shell Model (MCSM). The MCSM provides us with a breakthrough in shell model calculations: the structure of low-lying states can be studied with realistic interactions for a nearly unlimited variety of nuclei. Thus, the MCSM can contribute significantly to the study of nuclear masses. An application to N∼20 unstable nuclei far from the β-stability line is mentioned
Archimedes, the Free Monte Carlo simulator
Sellier, Jean Michel D
2012-01-01
Archimedes is the GNU package for Monte Carlo simulations of electron transport in semiconductor devices. The first release appeared in 2004 and since then it has been improved with many new features like quantum corrections, magnetic fields, new materials, GUI, etc. This document represents the first attempt to have a complete manual. Many of the Physics models implemented are described and a detailed description is presented to make the user able to write his/her own input deck. Please, feel free to contact the author if you want to contribute to the project.
Quasi-Monte Carlo methods for lattice systems. A first look
International Nuclear Information System (INIS)
We investigate the applicability of Quasi-Monte Carlo methods to Euclidean lattice systems for quantum mechanics in order to improve the asymptotic error behavior of observables for such theories. In most cases the error of an observable calculated by averaging over random observations generated from an ordinary Markov chain Monte Carlo simulation behaves like N-1/2, where N is the number of observations. By means of Quasi-Monte Carlo methods it is possible to improve this behavior for certain problems up to N-1. We adapted and applied this approach to simple systems like the quantum harmonic and anharmonic oscillator and verified an improved error scaling.
Quantum Permanents and Quantum Hafnians
Jing, Naihuan; Jian ZHANG
2015-01-01
Analogous to the quantum general linear group, a quantum group is investigated on which the quantum determinant is shown to be equal to the quantum permanent. The quantum Hafnian is then computed by a closely related quantum permanent. Similarly the quantum Pfaffian is proved to be identical to the quantum Hafnian on the quantum algebra.
MONTE-4 for Monte Carlo simulations with high performance
International Nuclear Information System (INIS)
The Monte Carlo machine MONTE-4, has been developed based on the architecture of existing supercomputer with a design philosophy to realize high performance in vector-parallel processing of Monte Carlo codes for particle transport problems. The effective performance of this Monte Carlo machine is presented through practical applications of multi-group criticality safety code KENO-IV and continuous-energy neutron/photon transport code MCNP. Ten times speedup has been obtained on MONTE-4 compared with the execution time in the scalar processing. (K.A.)
Monte Carlo photon benchmark problems
International Nuclear Information System (INIS)
Photon benchmark calculations have been performed to validate the MCNP Monte Carlo computer code. These are compared to both the COG Monte Carlo computer code and either experimental or analytic results. The calculated solutions indicate that the Monte Carlo method, and MCNP and COG in particular, can accurately model a wide range of physical problems. 8 refs., 5 figs
Theory of Quantum Annealing of an Ising Spin Glass
Santoro, Giuseppe E.; Martonak, Roman; Tosatti, Erio; Car, Roberto
2002-01-01
Probing the lowest energy configuration of a complex system by quantum annealing was recently found to be more effective than its classical, thermal counterpart. Comparing classical and quantum Monte Carlo annealing protocols on the random two-dimensional Ising model we confirm the superiority of quantum annealing relative to classical annealing. We also propose a theory of quantum annealing, based on a cascade of Landau-Zener tunneling events. For both classical and quantum annealing, the re...
Diffusion Monte Carlo: Exponentially inefficent for large systems?
Nemec, Norbert
2009-01-01
The computational cost of a Monte Carlo algorithm can only be meaningfully discussed when taking into account the magnitude of the resulting statistical error. Aiming for a fixed error per particle, we study the scaling behavior of the diffusion Monte Carlo method for large quantum systems. We identify the correlation within the population of walkers as the dominant scaling factor for large systems. While this factor is negligible for small and medium sized systems that are typically studied, it ultimately shows exponential scaling beyond system sizes that can be estimated straightforwardly for each specific system.
Energy Technology Data Exchange (ETDEWEB)
Wollaber, Allan Benton [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-06-16
This is a powerpoint presentation which serves as lecture material for the Parallel Computing summer school. It goes over the fundamentals of the Monte Carlo calculation method. The material is presented according to the following outline: Introduction (background, a simple example: estimating π), Why does this even work? (The Law of Large Numbers, The Central Limit Theorem), How to sample (inverse transform sampling, rejection), and An example from particle transport.
International Nuclear Information System (INIS)
The contributon Monte Carlo method is based on a new recipe to calculate target responses by means of volume integral of the contributon current in a region between the source and the detector. A comprehensive description of the method, its implementation in the general-purpose MCNP code, and results of the method for realistic nonhomogeneous, energy-dependent problems are presented. 23 figures, 10 tables
Optimization using quantum mechanics: quantum annealing through adiabatic evolution
International Nuclear Information System (INIS)
We review here some recent work in the field of quantum annealing, alias adiabatic quantum computation. The idea of quantum annealing is to perform optimization by a quantum adiabatic evolution which tracks the ground state of a suitable time-dependent Hamiltonian, where 'ℎ' is slowly switched off. We illustrate several applications of quantum annealing strategies, starting from textbook toy-models-double-well potentials and other one-dimensional examples, with and without disorder. These examples display in a clear way the crucial differences between classical and quantum annealing. We then discuss applications of quantum annealing to challenging hard optimization problems, such as the random Ising model, the travelling salesman problem and Boolean satisfiability problems. The techniques used to implement quantum annealing are either deterministic Schroedinger's evolutions, for the toy models, or path-integral Monte Carlo and Green's function Monte Carlo approaches, for the hard optimization problems. The crucial role played by disorder and the associated non-trivial Landau-Zener tunnelling phenomena is discussed and emphasized. (topical review)
Quantum Erasure: Quantum Interference Revisited
Walborn, Stephen P.; Cunha, Marcelo O Terra; Pádua, Sebastião; Monken, Carlos H.
2005-01-01
Recent experiments in quantum optics have shed light on the foundations of quantum physics. Quantum erasers - modified quantum interference experiments - show that quantum entanglement is responsible for the complementarity principle.
Bouabça, Thomas; Ben Amor, Nadia; Maynau, Daniel; Caffarel, Michel
2009-03-01
We report fixed-node diffusion Monte Carlo (FN-DMC) calculations of the singlet n →π∗ (CO) vertical transition of acrolein. The impact of the fixed-node approximation on the excitation energy is investigated. To do that, trial wave functions corresponding to various nodal patterns are used. They are constructed by using either a minimal complete-active-space self-consistent field (CASSCF) calculation involving an oxygen lone pair n and the π∗ (CO) molecular orbitals or a more complete set involving all the molecular orbitals expected to play a significant role in the excitation process. Calculations of both states have been performed with molecular orbitals optimized separately for each state via standard "state specific" CASSCF calculations or by using a common set of optimized orbitals ["state averaged" CASSCF calculations] whose effect is to introduce some important correlation between the nodal patterns of the two electronic states. To investigate the role of the basis set three different basis of increasing size have been employed. The comparative study based on the use of all possible combinations of basis sets, active spaces, and type of optimized molecular orbitals shows that the nodal error on the difference of energies is small when chemically relevant active space and state-averaged-type CASSCF wave functions are used, although the fixed-node error on the individual total energies involved can vary substantially. This remarkable result obtained for the acrolein suggests that FN-DMC calculations based on a simple strategy (use of standard ab initio wave functions and no Monte Carlo optimization of molecular orbital parameters) could be a working computational tool for computing electronic transition energies for more general systems.
Jazz Club
2012-01-01
The 5th edition of the "Monts Jura Jazz Festival" that will take place on September 21st and 22nd 2012 at the Esplanade du Lac in Divonne-les-Bains. This festival is organized by the "CERN Jazz Club" with the support of the "CERN Staff Association". This festival is a major musical event in the French/Swiss area and proposes a world class program with jazz artists such as D.Lockwood and D.Reinhardt. More information on http://www.jurajazz.com.
2012-01-01
The 5th edition of the "Monts Jura Jazz Festival" will take place at the Esplanade du Lac in Divonne-les-Bains, France on September 21 and 22. This festival organized by the CERN Jazz Club and supported by the CERN Staff Association is becoming a major musical event in the Geneva region. International Jazz artists like Didier Lockwood and David Reinhardt are part of this year outstanding program. Full program and e-tickets are available on the festival website. Don't miss this great festival!
Classical and quantum anisotropic Heisenberg antiferromagnets
Directory of Open Access Journals (Sweden)
W. Selke
2009-01-01
Full Text Available We study classical and quantum Heisenberg antiferromagnets with exchange anisotropy of XXZ-type and crystal field single-ion terms of quadratic and quartic form in a field. The magnets display a variety of phases, including the spin-flop (or, in the quantum case, spin-liquid and biconical (corresponding, in the quantum lattice gas description, to supersolid phases. Applying ground-state considerations, Monte Carlo and density matrix renormalization group methods, the impact of quantum effects and lattice dimension is analysed. Interesting critical and multicritical behaviour may occur at quantum and thermal phase transitions.
Monte Carlo Simulation in Statistical Physics An Introduction
Binder, Kurt
2010-01-01
Monte Carlo Simulation in Statistical Physics deals with the computer simulation of many-body systems in condensed-matter physics and related fields of physics, chemistry and beyond, to traffic flows, stock market fluctuations, etc.). Using random numbers generated by a computer, probability distributions are calculated, allowing the estimation of the thermodynamic properties of various systems. This book describes the theoretical background to several variants of these Monte Carlo methods and gives a systematic presentation from which newcomers can learn to perform such simulations and to analyze their results. The fifth edition covers Classical as well as Quantum Monte Carlo methods. Furthermore a new chapter on the sampling of free-energy landscapes has been added. To help students in their work a special web server has been installed to host programs and discussion groups (http://wwwcp.tphys.uni-heidelberg.de). Prof. Binder was awarded the Berni J. Alder CECAM Award for Computational Physics 2001 as well ...
Applicability of quasi-Monte Carlo for lattice systems
Energy Technology Data Exchange (ETDEWEB)
Ammon, Andreas [Berlin Humboldt-Univ. (Germany). Dept. of Physics; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Hartung, Tobias [King' s College London (United Kingdom). Dept. of Mathematics; Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Leovey, Hernan; Griewank, Andreas [Berlin Humboldt-Univ. (Germany). Dept. of Mathematics; Mueller-Preussker, Michael [Berlin Humboldt-Univ. (Germany). Dept. of Physics
2013-11-15
This project investigates the applicability of quasi-Monte Carlo methods to Euclidean lattice systems in order to improve the asymptotic error scaling of observables for such theories. The error of an observable calculated by averaging over random observations generated from ordinary Monte Carlo simulations scales like N{sup -1/2}, where N is the number of observations. By means of quasi-Monte Carlo methods it is possible to improve this scaling for certain problems to N{sup -1}, or even further if the problems are regular enough. We adapted and applied this approach to simple systems like the quantum harmonic and anharmonic oscillator and verified an improved error scaling of all investigated observables in both cases.
Applicability of quasi-Monte Carlo for lattice systems
International Nuclear Information System (INIS)
This project investigates the applicability of quasi-Monte Carlo methods to Euclidean lattice systems in order to improve the asymptotic error scaling of observables for such theories. The error of an observable calculated by averaging over random observations generated from ordinary Monte Carlo simulations scales like N-1/2, where N is the number of observations. By means of quasi-Monte Carlo methods it is possible to improve this scaling for certain problems to N-1, or even further if the problems are regular enough. We adapted and applied this approach to simple systems like the quantum harmonic and anharmonic oscillator and verified an improved error scaling of all investigated observables in both cases.
Applicability of Quasi-Monte Carlo for lattice systems
Ammon, Andreas; Jansen, Karl; Leovey, Hernan; Griewank, Andreas; Müller-Preussker, Micheal
2013-01-01
This project investigates the applicability of quasi-Monte Carlo methods to Euclidean lattice systems in order to improve the asymptotic error scaling of observables for such theories. The error of an observable calculated by averaging over random observations generated from ordinary Monte Carlo simulations scales like $N^{-1/2}$, where $N$ is the number of observations. By means of quasi-Monte Carlo methods it is possible to improve this scaling for certain problems to $N^{-1}$, or even further if the problems are regular enough. We adapted and applied this approach to simple systems like the quantum harmonic and anharmonic oscillator and verified an improved error scaling of all investigated observables in both cases.
Optimization of Monte Carlo simulations
Bryskhe, Henrik
2009-01-01
This thesis considers several different techniques for optimizing Monte Carlo simulations. The Monte Carlo system used is Penelope but most of the techniques are applicable to other systems. The two mayor techniques are the usage of the graphics card to do geometry calculations, and raytracing. Using graphics card provides a very efficient way to do fast ray and triangle intersections. Raytracing provides an approximation of Monte Carlo simulation but is much faster to perform. A program was ...
Monte Carlo wave packet propagators for multidimensional vibrational spectroscopy
Samsonyuk, Andriy
2013-01-01
A direct Monte Carlo wave packet sampling method for Liouville space pathways, based on the solution of the quantum stochastic differential equation in a doubled Hilbert space, was developed to widen the scope of nonlinear spectroscopy simulations. Using this method we can: compute third order infrared response functions for systems with thousands of states, which was not possible before; simulate a very broad range of experiments with any number of pulse interactions; reduce the computationa...
Monte Carlo numerical study of lattice field theories
International Nuclear Information System (INIS)
The authors are interested in the exact first-principle calculations of quantum field theories which are indeed exact ones. For quantum chromodynamics (QCD) at low energy scale, a nonperturbation method is needed, and the only known such method is the lattice method. The path integral can be evaluated by putting a system on a finite 4-dimensional volume and discretizing space time continuum into finite points, lattice. The continuum limit is taken by making the lattice infinitely fine. For evaluating such a finite-dimensional integral, the Monte Carlo numerical estimation of the path integral can be obtained. The calculation of light hadron mass in quenched lattice QCD with staggered quarks, 3-dimensional Thirring model calculation and the development of self-test Monte Carlo method have been carried out by using the RIKEN supercomputer. The motivation of this study, lattice QCD formulation, continuum limit, Monte Carlo update, hadron propagator, light hadron mass, auto-correlation and source size dependence are described on lattice QCD. The phase structure of the 3-dimensional Thirring model for a small 83 lattice has been mapped. The discussion on self-test Monte Carlo method is described again. (K.I.)
Transforming quantum operations: quantum supermaps
Chiribella, G.; D'Ariano, G. M.; Perinotti, P.
2008-01-01
We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and measurements, quantum supermaps describe all possible transformations between elementary quantum objects (quantum systems as well as quantum devices). After giving the axiomatic definition of supermap, we prove a realization theorem, which shows that any sup...
Quantum correlation via quantum coherence
Yu, Chang-shui; Zhang, Yang; Zhao, Haiqing
2014-01-01
Quantum correlation includes quantum entanglement and quantum discord. Both entanglement and discord have a common necessary condition--------quantum coherence or quantum superposition. In this paper, we attempt to give an alternative understanding of how quantum correlation is related to quantum coherence. We divide the coherence of a quantum state into several classes and find the complete coincidence between geometric (symmetric and asymmetric) quantum discords and some particular classes ...
Controlling quantum information
Landahl, Andrew John
Quantum information science explores ways in which quantum physical laws can be harnessed to control the acquisition, transmission, protection, and processing of information. This field has seen explosive growth in the past several years from progress on both theoretical and experimental fronts. Essential to this endeavor are methods for controlling quantum information. In this thesis, I present three new approaches for controlling quantum information. First, I present a new protocol for continuously protecting unknown quantum states from noise. This protocol combines and expands ideas from the theories of quantum error correction and quantum feedback control. The result can outperform either approach by itself. I generalize this protocol to all known quantum stabilizer codes, and study its application to the three-qubit repetition code in detail via Monte Carlo simulations. Next, I present several new protocols for controlling quantum information that are fault-tolerant. These protocols require only local quantum processing due to the topological properties of the quantum error correcting codes upon which they are built. I show that each protocol's fault-dependence behavior exhibits an order-disorder phase transition when mapped onto an associated statistical-mechanical model. I review the critical error rates of these protocols found by numerical study of the associated models, and I present new analytic bounds for them using a self-avoiding random walk argument. Moreover, I discuss fault-tolerant procedures for encoding, error-correction, computing, and decoding quantum information using these protocols, and calculate the accuracy threshold of fault-tolerant quantum memory for protocols using them. I end by presenting a new class of quantum algorithms that solve combinatorial optimization problems solely by measurement. I compute the running times of these algorithms by establishing an explicit dynamical model for the measurement process. This model, the
Collective excitations of nuclei in the Monte-Carlo shell model
International Nuclear Information System (INIS)
The formulation and recent applications of the Quantum Monte Carlo diagonalization (QMCD) method are reported. The QMCD has been proposed for solving the quantum many-body interacting systems, providing us with energy eigenvalues, transition matrix elements and wave functions. Its application to the nuclear shell model is referred to as the Monte Carlo Shell Model. By the Monte Carlo Shell Model calculations, the level structure of low-lying states can be studied with realistic interactions, providing a useful tool for nuclear spectroscopy. The Monte Carlo Shell Model has been applied to the study of a variety of nuclei, and can be characterized as the importance truncation scheme to the full diagonalization which is infeasible in many cases due to extremely large dimensions. Applications to the study of quadrupole collective states are discussed. (author)
International Nuclear Information System (INIS)
The course of ''Monte Carlo Techniques'' will try to give a general overview of how to build up a method based on a given theory, allowing you to compare the outcome of an experiment with that theory. Concepts related with the construction of the method, such as, random variables, distributions of random variables, generation of random variables, random-based numerical methods, will be introduced in this course. Examples of some of the current theories in High Energy Physics describing the e+e- annihilation processes (QED, Electro-Weak, QCD) will also be briefly introduced. A second step in the employment of this method is related to the detector. The interactions that a particle could have along its way, through the detector as well as the response of the different materials which compound the detector will be quoted in this course. An example of detector at LEP era, in which these techniques are being applied, will close the course. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Marcus, Ryan C. [Los Alamos National Laboratory
2012-07-25
MCMini is a proof of concept that demonstrates the possibility for Monte Carlo neutron transport using OpenCL with a focus on performance. This implementation, written in C, shows that tracing particles and calculating reactions on a 3D mesh can be done in a highly scalable fashion. These results demonstrate a potential path forward for MCNP or other Monte Carlo codes.
Monte Carlo Methods in Physics
International Nuclear Information System (INIS)
Method of Monte Carlo integration is reviewed briefly and some of its applications in physics are explained. A numerical experiment on random generators used in the monte Carlo techniques is carried out to show the behavior of the randomness of various methods in generating them. To account for the weight function involved in the Monte Carlo, the metropolis method is used. From the results of the experiment, one can see that there is no regular patterns of the numbers generated, showing that the program generators are reasonably good, while the experimental results, shows a statistical distribution obeying statistical distribution law. Further some applications of the Monte Carlo methods in physics are given. The choice of physical problems are such that the models have available solutions either in exact or approximate values, in which comparisons can be mode, with the calculations using the Monte Carlo method. Comparison show that for the models to be considered, good agreement have been obtained
Quantum Instantons and Quantum Chaos
Jirari, H.; Kröger, H.; Luo, X. Q.; Moriarty, K. J. M.; Rubin, S. G.
1999-01-01
Based on a closed form expression for the path integral of quantum transition amplitudes, we suggest rigorous definitions of both, quantum instantons and quantum chaos. As an example we compute the quantum instanton of the double well potential.
International Nuclear Information System (INIS)
The statistical error is ineluctable in any measurement. Quantum techniques, especially with the development of quantum information, can help us squeeze the statistical error and enhance the precision of measurement. In a quantum system, there are some quantum parameters, such as the quantum state, quantum operator, and quantum dimension, which have no classical counterparts. So quantum metrology deals with not only the traditional parameters, but also the quantum parameters. Quantum metrology includes two important parts: measuring the physical parameters with a precision beating the classical physics limit and measuring the quantum parameters precisely. In this review, we will introduce how quantum characters (e.g., squeezed state and quantum entanglement) yield a higher precision, what the research areas are scientists most interesting in, and what the development status of quantum metrology and its perspectives are. (topical review - quantum information)
Quantum Computation and Quantum Information
Wang, Yazhen
2012-01-01
Quantum computation and quantum information are of great current interest in computer science, mathematics, physical sciences and engineering. They will likely lead to a new wave of technological innovations in communication, computation and cryptography. As the theory of quantum physics is fundamentally stochastic, randomness and uncertainty are deeply rooted in quantum computation, quantum simulation and quantum information. Consequently quantum algorithms are random in nature, and quantum ...
Parallelizing Monte Carlo with PMC
Energy Technology Data Exchange (ETDEWEB)
Rathkopf, J.A.; Jones, T.R.; Nessett, D.M.; Stanberry, L.C.
1994-11-01
PMC (Parallel Monte Carlo) is a system of generic interface routines that allows easy porting of Monte Carlo packages of large-scale physics simulation codes to Massively Parallel Processor (MPP) computers. By loading various versions of PMC, simulation code developers can configure their codes to run in several modes: serial, Monte Carlo runs on the same processor as the rest of the code; parallel, Monte Carlo runs in parallel across many processors of the MPP with the rest of the code running on other MPP processor(s); distributed, Monte Carlo runs in parallel across many processors of the MPP with the rest of the code running on a different machine. This multi-mode approach allows maintenance of a single simulation code source regardless of the target machine. PMC handles passing of messages between nodes on the MPP, passing of messages between a different machine and the MPP, distributing work between nodes, and providing independent, reproducible sequences of random numbers. Several production codes have been parallelized under the PMC system. Excellent parallel efficiency in both the distributed and parallel modes results if sufficient workload is available per processor. Experiences with a Monte Carlo photonics demonstration code and a Monte Carlo neutronics package are described.
Georgescu, I. M.; Ashhab, S.; Nori, Franco
2013-01-01
Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficulty may be overcome by using some controllable quantum system to study another less controllable or accessible quantum system, i.e., quantum simulation. Quantum simulation promises to have applications in the study of many problems in, e.g., condensed-matter physics, high-energy physics, atomic physics, quantum chemistry and cosmology. Quantum simulat...
Mosca, Michele
2009-01-01
One of the earliest cryptographic applications of quantum information was to create quantum digital cash that could not be counterfeited. In this paper, we describe a new type of quantum money: quantum coins, where all coins of the same denomination are represented by identical quantum states. We state desirable security properties such as anonymity and unforgeability and propose two candidate quantum coin schemes: one using black box operations, and another using blind quantum computation.
Path integral Monte Carlo and the electron gas
Brown, Ethan W.
Path integral Monte Carlo is a proven method for accurately simulating quantum mechanical systems at finite-temperature. By stochastically sampling Feynman's path integral representation of the quantum many-body density matrix, path integral Monte Carlo includes non-perturbative effects like thermal fluctuations and particle correlations in a natural way. Over the past 30 years, path integral Monte Carlo has been successfully employed to study the low density electron gas, high-pressure hydrogen, and superfluid helium. For systems where the role of Fermi statistics is important, however, traditional path integral Monte Carlo simulations have an exponentially decreasing efficiency with decreased temperature and increased system size. In this thesis, we work towards improving this efficiency, both through approximate and exact methods, as specifically applied to the homogeneous electron gas. We begin with a brief overview of the current state of atomic simulations at finite-temperature before we delve into a pedagogical review of the path integral Monte Carlo method. We then spend some time discussing the one major issue preventing exact simulation of Fermi systems, the sign problem. Afterwards, we introduce a way to circumvent the sign problem in PIMC simulations through a fixed-node constraint. We then apply this method to the homogeneous electron gas at a large swatch of densities and temperatures in order to map out the warm-dense matter regime. The electron gas can be a representative model for a host of real systems, from simple medals to stellar interiors. However, its most common use is as input into density functional theory. To this end, we aim to build an accurate representation of the electron gas from the ground state to the classical limit and examine its use in finite-temperature density functional formulations. The latter half of this thesis focuses on possible routes beyond the fixed-node approximation. As a first step, we utilize the variational
Quantum Genetics, Quantum Automata and Quantum Computation
Baianu, Professor I. C.
2004-01-01
The concepts of quantum automata and quantum computation are studied in the context of quantum genetics and genetic networks with nonlinear dynamics. In a previous publication (Baianu,1971a) the formal concept of quantum automaton was introduced and its possible implications for genetic and metabolic activities in living cells and organisms were considered. This was followed by a report on quantum and abstract, symbolic computation based on the theory of categories, functors and natural trans...
Le Gouët, Jean-Louis; Moiseev, Sergey
2012-06-01
Interaction of quantum radiation with multi-particle ensembles has sparked off intense research efforts during the past decade. Emblematic of this field is the quantum memory scheme, where a quantum state of light is mapped onto an ensemble of atoms and then recovered in its original shape. While opening new access to the basics of light-atom interaction, quantum memory also appears as a key element for information processing applications, such as linear optics quantum computation and long-distance quantum communication via quantum repeaters. Not surprisingly, it is far from trivial to practically recover a stored quantum state of light and, although impressive progress has already been accomplished, researchers are still struggling to reach this ambitious objective. This special issue provides an account of the state-of-the-art in a fast-moving research area that makes physicists, engineers and chemists work together at the forefront of their discipline, involving quantum fields and atoms in different media, magnetic resonance techniques and material science. Various strategies have been considered to store and retrieve quantum light. The explored designs belong to three main—while still overlapping—classes. In architectures derived from photon echo, information is mapped over the spectral components of inhomogeneously broadened absorption bands, such as those encountered in rare earth ion doped crystals and atomic gases in external gradient magnetic field. Protocols based on electromagnetic induced transparency also rely on resonant excitation and are ideally suited to the homogeneous absorption lines offered by laser cooled atomic clouds or ion Coulomb crystals. Finally off-resonance approaches are illustrated by Faraday and Raman processes. Coupling with an optical cavity may enhance the storage process, even for negligibly small atom number. Multiple scattering is also proposed as a way to enlarge the quantum interaction distance of light with matter. The
Quantum Distinction: Quantum Distinctiones!
Directory of Open Access Journals (Sweden)
Dainis ZEPS
2009-07-01
Full Text Available How many distinctions, in Latin, quantum distinctions have? We suggest approach of anthropic principle based on anthropic reference system which should be applied equally both in theoretical physics and in mathematics. We come to principle that within reference system of life subject of mathematics (that of thinking should be equated with subject of physics (that of nature. For this reason we enter notions of series of distinctions, quantum distinction, and argue that quantum distinction may be considered as freedom of motion.
Chang, Mou-Hsiung
2015-01-01
The classical probability theory initiated by Kolmogorov and its quantum counterpart, pioneered by von Neumann, were created at about the same time in the 1930s, but development of the quantum theory has trailed far behind. Although highly appealing, the quantum theory has a steep learning curve, requiring tools from both probability and analysis and a facility for combining the two viewpoints. This book is a systematic, self-contained account of the core of quantum probability and quantum stochastic processes for graduate students and researchers. The only assumed background is knowledge of the basic theory of Hilbert spaces, bounded linear operators, and classical Markov processes. From there, the book introduces additional tools from analysis, and then builds the quantum probability framework needed to support applications to quantum control and quantum information and communication. These include quantum noise, quantum stochastic calculus, stochastic quantum differential equations, quantum Markov semigrou...
Gisin, Nicolas; Ribordy, Grégoire; Tittel, Wolfgang; Zbinden, Hugo
2002-01-01
Quantum cryptography could well be the first application of quantum mechanics at the single-quantum level. The rapid progress in both theory and experiment in recent years is reviewed, with emphasis on open questions and technological issues.
Monte Carlo: in the beginning and some great expectations
Energy Technology Data Exchange (ETDEWEB)
Metropolis, N.
1985-01-01
The central theme will be on the historical setting and origins of the Monte Carlo Method. The scene was post-war Los Alamos Scientific Laboratory. There was an inevitability about the Monte Carlo Event: the ENIAC had recently enjoyed its meteoric rise (on a classified Los Alamos problem); Stan Ulam had returned to Los Alamos; John von Neumann was a frequent visitor. Techniques, algorithms, and applications developed rapidly at Los Alamos. Soon, the fascination of the Method reached wider horizons. The first paper was submitted for publication in the spring of 1949. In the summer of 1949, the first open conference was held at the University of California at Los Angeles. Of some interst perhaps is an account of Fermi's earlier, independent application in neutron moderation studies while at the University of Rome. The quantum leap expected with the advent of massively parallel processors will provide stimuli for very ambitious applications of the Monte Carlo Method in disciplines ranging from field theories to cosmology, including more realistic models in the neurosciences. A structure of multi-instruction sets for parallel processing is ideally suited for the Monte Carlo approach. One may even hope for a modest hardening of the soft sciences.
Monte Carlo: in the beginning and some great expectations
International Nuclear Information System (INIS)
The central theme will be on the historical setting and origins of the Monte Carlo Method. The scene was post-war Los Alamos Scientific Laboratory. There was an inevitability about the Monte Carlo Event: the ENIAC had recently enjoyed its meteoric rise (on a classified Los Alamos problem); Stan Ulam had returned to Los Alamos; John von Neumann was a frequent visitor. Techniques, algorithms, and applications developed rapidly at Los Alamos. Soon, the fascination of the Method reached wider horizons. The first paper was submitted for publication in the spring of 1949. In the summer of 1949, the first open conference was held at the University of California at Los Angeles. Of some interst perhaps is an account of Fermi's earlier, independent application in neutron moderation studies while at the University of Rome. The quantum leap expected with the advent of massively parallel processors will provide stimuli for very ambitious applications of the Monte Carlo Method in disciplines ranging from field theories to cosmology, including more realistic models in the neurosciences. A structure of multi-instruction sets for parallel processing is ideally suited for the Monte Carlo approach. One may even hope for a modest hardening of the soft sciences
Observations on variational and projector Monte Carlo methods
International Nuclear Information System (INIS)
Variational Monte Carlo and various projector Monte Carlo (PMC) methods are presented in a unified manner. Similarities and differences between the methods and choices made in designing the methods are discussed. Both methods where the Monte Carlo walk is performed in a discrete space and methods where it is performed in a continuous space are considered. It is pointed out that the usual prescription for importance sampling may not be advantageous depending on the particular quantum Monte Carlo method used and the observables of interest, so alternate prescriptions are presented. The nature of the sign problem is discussed for various versions of PMC methods. A prescription for an exact PMC method in real space, i.e., a method that does not make a fixed-node or similar approximation and does not have a finite basis error, is presented. This method is likely to be practical for systems with a small number of electrons. Approximate PMC methods that are applicable to larger systems and go beyond the fixed-node approximation are also discussed
Wu, Lian-Ao; Lidar, Daniel A.
2005-01-01
When quantum communication networks proliferate they will likely be subject to a new type of attack: by hackers, virus makers, and other malicious intruders. Here we introduce the concept of "quantum malware" to describe such human-made intrusions. We offer a simple solution for storage of quantum information in a manner which protects quantum networks from quantum malware. This solution involves swapping the quantum information at random times between the network and isolated, distributed an...
Gisin, Nicolas; Thew, Rob
2007-01-01
Quantum communication, and indeed quantum information in general, has changed the way we think about quantum physics. In 1984 and 1991, the first protocol for quantum cryptography and the first application of quantum non-locality, respectively, attracted a diverse field of researchers in theoretical and experimental physics, mathematics and computer science. Since then we have seen a fundamental shift in how we understand information when it is encoded in quantum systems. We review the curren...
Ronnie Kosloff
2013-01-01
Quantum thermodynamics addresses the emergence of thermodynamic laws from quantum mechanics. The viewpoint advocated is based on the intimate connection of quantum thermodynamics with the theory of open quantum systems. Quantum mechanics inserts dynamics into thermodynamics, giving a sound foundation to finite-time-thermodynamics. The emergence of the 0-law, I-law, II-law and III-law of thermodynamics from quantum considerations is presented. The emphasis is on consistency between the two the...
Borovitskaya, Elena
2002-01-01
In this book, leading experts on quantum dot theory and technology provide comprehensive reviews of all aspects of quantum dot systems. The following topics are covered: (1) energy states in quantum dots, including the effects of strain and many-body effects; (2) self-assembly and self-ordering of quantum dots in semiconductor systems; (3) growth, structures, and optical properties of III-nitride quantum dots; (4) quantum dot lasers. Contents: Low-Dimensional Systems (E Borovitskaya & M S Shur); Energy States in Quantum Dots (A J Williamson); Self-Organized Quantum Dots (A R Woll et al.); Grow
Khrennikov, Andrei
2014-01-01
The present wave of interest in quantum foundations is caused by the tremendous development of quantum information science and its applications to quantum computing and quantum communication. It has become clear that some of the difficulties encountered in realizations of quantum information processing have roots at the very fundamental level. To solve such problems, quantum theory has to be reconsidered. This book is devoted to the analysis of the probabilistic structure of quantum theory, probing the limits of classical probabilistic representation of quantum phenomena.
Estimation of beryllium ground state energy by Monte Carlo simulation
International Nuclear Information System (INIS)
Quantum Monte Carlo method represent a powerful and broadly applicable computational tool for finding very accurate solution of the stationary Schrödinger equation for atoms, molecules, solids and a variety of model systems. Using variational Monte Carlo method we have calculated the ground state energy of the Beryllium atom. Our calculation are based on using a modified four parameters trial wave function which leads to good result comparing with the few parameters trial wave functions presented before. Based on random Numbers we can generate a large sample of electron locations to estimate the ground state energy of Beryllium. Our calculation gives good estimation for the ground state energy of the Beryllium atom comparing with the corresponding exact data
Estimation of beryllium ground state energy by Monte Carlo simulation
Energy Technology Data Exchange (ETDEWEB)
Kabir, K. M. Ariful [Department of Physical Sciences, School of Engineering and Computer Science, Independent University, Bangladesh (IUB) Dhaka (Bangladesh); Halder, Amal [Department of Mathematics, University of Dhaka Dhaka (Bangladesh)
2015-05-15
Quantum Monte Carlo method represent a powerful and broadly applicable computational tool for finding very accurate solution of the stationary Schrödinger equation for atoms, molecules, solids and a variety of model systems. Using variational Monte Carlo method we have calculated the ground state energy of the Beryllium atom. Our calculation are based on using a modified four parameters trial wave function which leads to good result comparing with the few parameters trial wave functions presented before. Based on random Numbers we can generate a large sample of electron locations to estimate the ground state energy of Beryllium. Our calculation gives good estimation for the ground state energy of the Beryllium atom comparing with the corresponding exact data.
Nuclear pairing within a configuration-space Monte Carlo approach
Lingle, Mark; Volya, Alexander
2015-06-01
Pairing correlations in nuclei play a decisive role in determining nuclear drip lines, binding energies, and many collective properties. In this work a new configuration-space Monte Carlo (CSMC) method for treating nuclear pairing correlations is developed, implemented, and demonstrated. In CSMC the Hamiltonian matrix is stochastically generated in Krylov subspace, resulting in the Monte Carlo version of Lanczos-like diagonalization. The advantages of this approach over other techniques are discussed; the absence of the fermionic sign problem, probabilistic interpretation of quantum-mechanical amplitudes, and ability to handle truly large-scale problems with defined precision and error control are noteworthy merits of CSMC. The features of our CSMC approach are shown using models and realistic examples. Special attention is given to difficult limits: situations with nonconstant pairing strengths, cases with nearly degenerate excited states, limits when pairing correlations in finite systems are weak, and problems when the relevant configuration space is large.
Fixed-Node Diffusion Monte Carlo of Lithium Systems
Rasch, Kevin
2015-01-01
We study lithium systems over a range of number of atoms, e.g., atomic anion, dimer, metallic cluster, and body-centered cubic crystal by the diffusion Monte Carlo method. The calculations include both core and valence electrons in order to avoid any possible impact by pseudo potentials. The focus of the study is the fixed-node errors, and for that purpose we test several orbital sets in order to provide the most accurate nodal hyper surfaces. We compare our results to other high accuracy calculations wherever available and to experimental results so as to quantify the the fixed-node errors. The results for these Li systems show that fixed-node quantum Monte Carlo achieves remarkably high accuracy total energies and recovers 97-99 % of the correlation energy.
Quasi-Monte Carlo methods for lattice systems. A first look
Energy Technology Data Exchange (ETDEWEB)
Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Leovey, H.; Griewank, A. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Mathematik; Nube, A. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Mueller-Preussker, M. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik
2013-02-15
We investigate the applicability of Quasi-Monte Carlo methods to Euclidean lattice systems for quantum mechanics in order to improve the asymptotic error behavior of observables for such theories. In most cases the error of an observable calculated by averaging over random observations generated from an ordinary Markov chain Monte Carlo simulation behaves like N{sup -1/2}, where N is the number of observations. By means of Quasi-Monte Carlo methods it is possible to improve this behavior for certain problems up to N{sup -1}. We adapted and applied this approach to simple systems like the quantum harmonic and anharmonic oscillator and verified an improved error scaling.
Nonlinear Dynamics In Quantum Physics -- Quantum Chaos and Quantum Instantons
Kröger, H.
2003-01-01
We discuss the recently proposed quantum action - its interpretation, its motivation, its mathematical properties and its use in physics: quantum mechanical tunneling, quantum instantons and quantum chaos.
Stochastic solution to quantum dynamics
John, Sarah; Wilson, John W.
1994-01-01
The quantum Liouville equation in the Wigner representation is solved numerically by using Monte Carlo methods. For incremental time steps, the propagation is implemented as a classical evolution in phase space modified by a quantum correction. The correction, which is a momentum jump function, is simulated in the quasi-classical approximation via a stochastic process. The technique, which is developed and validated in two- and three- dimensional momentum space, extends an earlier one-dimensional work. Also, by developing a new algorithm, the application to bound state motion in an anharmonic quartic potential shows better agreement with exact solutions in two-dimensional phase space.
Quantum Optics with Quantum Gases
Mekhov, Igor B.; Ritsch, Helmut
2009-01-01
Quantum optics with quantum gases represents a new field, where the quantum nature of both light and ultracold matter plays equally important role. Only very recently this ultimate quantum limit of light-matter interaction became feasible experimentally. In traditional quantum optics, the cold atoms are considered classically, whereas, in quantum atom optics, the light is used as an essentially classical axillary tool. On the one hand, the quantization of optical trapping potentials can signi...
Monte Carlo approaches to effective field theories
International Nuclear Information System (INIS)
In this paper, we explore the application of continuum Monte Carlo methods to effective field theory models. Effective field theories, in this context, are those in which a Fock space decomposition of the state is useful. These problems arise both in nuclear and condensed matter physica. In nuclear physics, much work has been done on effective field theories of mesons and baryons. While the theories are not fundamental, they should be able to describe nuclear properties at low energy and momentum scales. After describing the methods, we solve two simple scalar field theory problems; the polaron and two nucleons interacting through scalar meson exchange. The methods presented here are rather straightforward extensions of methods used to solve quantum mechanics problems. Monte Carlo methods are used to avoid the truncation inherent in a Tamm-Dancoff approach and its associated difficulties. Nevertheless, the methods will be most valuable when the Fock space decomposition of the states is useful. Hence, while they are not intended for ab initio studies of QCD, they may prove valuable in studies of light nuclei, or for systems of interacting electrons and phonons. In these problems a Fock space decomposition can be used to reduce the number of degrees of freedom and to retain the rotational symmetries exactly. The problems we address here are comparatively simple, but offer useful initial tests of the method. We present results for the polaron and two non-relativistic nucleons interacting through scalar meson exchange. In each case, it is possible to integrate out the boson degrees of freedom exactly, and obtain a retarded form of the action that depends only upon the fermion paths. Here we keep the explicit bosons, though, since we would like to retain information about the boson components of the states and it will be necessary to keep these components in order to treat non-scalar of interacting bosonic fields
Simulation and understanding of quantum crystals
Cazorla, Claudio
2016-01-01
Quantum crystals abound in the whole range of solid-state species. Below a certain threshold temperature the physical behavior of rare gases (4He and Ne), molecular solids (H2 and CH4), and some ionic (LiH), covalent (graphite), and metallic (Li) crystals can be only explained in terms of quantum nuclear effects (QNE). A detailed comprehension of the nature of quantum solids is critical for achieving progress in a number of fundamental and applied scientific fields like, for instance, planetary sciences, hydrogen storage, nuclear energy, quantum computing, and nanoelectronics. This review describes the current physical understanding of quantum crystals and the wide variety of simulation techniques that are used to investigate them. Relevant aspects in these materials such as phase transformations, energy and structural properties, elasticity, and the effects of crystalline defects and dimensionality, are discussed thoroughly. An introduction to quantum Monte Carlo techniques, which in the present context are ...
Proton Upset Monte Carlo Simulation
O'Neill, Patrick M.; Kouba, Coy K.; Foster, Charles C.
2009-01-01
The Proton Upset Monte Carlo Simulation (PROPSET) program calculates the frequency of on-orbit upsets in computer chips (for given orbits such as Low Earth Orbit, Lunar Orbit, and the like) from proton bombardment based on the results of heavy ion testing alone. The software simulates the bombardment of modern microelectronic components (computer chips) with high-energy (.200 MeV) protons. The nuclear interaction of the proton with the silicon of the chip is modeled and nuclear fragments from this interaction are tracked using Monte Carlo techniques to produce statistically accurate predictions.
Quantum Chaos and Quantum Computers
Shepelyansky, D L
2001-01-01
The standard generic quantum computer model is studied analytically and numerically and the border for emergence of quantum chaos, induced by imperfections and residual inter-qubit couplings, is determined. This phenomenon appears in an isolated quantum computer without any external decoherence. The onset of quantum chaos leads to quantum computer hardware melting, strong quantum entropy growth and destruction of computer operability. The time scales for development of quantum chaos and ergodicity are determined. In spite the fact that this phenomenon is rather dangerous for quantum computing it is shown that the quantum chaos border for inter-qubit coupling is exponentially larger than the energy level spacing between quantum computer eigenstates and drops only linearly with the number of qubits n. As a result the ideal multi-qubit structure of the computer remains rather robust against imperfections. This opens a broad parameter region for a possible realization of quantum computer. The obtained results are...
International Nuclear Information System (INIS)
The following topics are dealt with: Artificial atoms and molecules, tailored from solids, fractional flux quanta, molecular magnets, controlled interaction in quantum gases, the theory of quantum correlations in mott matter, cold gases, and mesoscopic systems, Bose-Einstein condensates on the chip, on the route to the quantum computer, a quantum computer in diamond. (HSI)
Communication: Water on hexagonal boron nitride from diffusion Monte Carlo
Energy Technology Data Exchange (ETDEWEB)
Al-Hamdani, Yasmine S.; Ma, Ming; Michaelides, Angelos, E-mail: angelos.michaelides@ucl.ac.uk [Thomas Young Centre and London Centre for Nanotechnology, 17–19 Gordon Street, London WC1H 0AH (United Kingdom); Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ (United Kingdom); Alfè, Dario [Thomas Young Centre and London Centre for Nanotechnology, 17–19 Gordon Street, London WC1H 0AH (United Kingdom); Department of Earth Sciences, University College London, Gower Street, London WC1E 6BT (United Kingdom); Lilienfeld, O. Anatole von [Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials, Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel (Switzerland); Argonne Leadership Computing Facility, Argonne National Laboratories, 9700 S. Cass Avenue Argonne, Lemont, Illinois 60439 (United States)
2015-05-14
Despite a recent flurry of experimental and simulation studies, an accurate estimate of the interaction strength of water molecules with hexagonal boron nitride is lacking. Here, we report quantum Monte Carlo results for the adsorption of a water monomer on a periodic hexagonal boron nitride sheet, which yield a water monomer interaction energy of −84 ± 5 meV. We use the results to evaluate the performance of several widely used density functional theory (DFT) exchange correlation functionals and find that they all deviate substantially. Differences in interaction energies between different adsorption sites are however better reproduced by DFT.
Monte Carlo simulation of a prototype photodetector used in radiotherapy
Kausch, C; Albers, D; Schmidt, R; Schreiber, B
2000-01-01
The imaging performance of prototype electronic portal imaging devices (EPID) has been investigated. Monte Carlo simulations have been applied to calculate the modulation transfer function (MTF( f )), the noise power spectrum (NPS( f )) and the detective quantum efficiency (DQE( f )) for different new type of EPIDs, which consist of a detector combination of metal or polyethylene (PE), a phosphor layer of Gd sub 2 O sub 2 S and a flat array of photodiodes. The simulated results agree well with measurements. Based on simulated results, possible optimization of these devices is discussed.
Communication: Water on hexagonal boron nitride from diffusion Monte Carlo
International Nuclear Information System (INIS)
Despite a recent flurry of experimental and simulation studies, an accurate estimate of the interaction strength of water molecules with hexagonal boron nitride is lacking. Here, we report quantum Monte Carlo results for the adsorption of a water monomer on a periodic hexagonal boron nitride sheet, which yield a water monomer interaction energy of −84 ± 5 meV. We use the results to evaluate the performance of several widely used density functional theory (DFT) exchange correlation functionals and find that they all deviate substantially. Differences in interaction energies between different adsorption sites are however better reproduced by DFT
Lanzagorta, Marco
2011-01-01
This book offers a concise review of quantum radar theory. Our approach is pedagogical, making emphasis on the physics behind the operation of a hypothetical quantum radar. We concentrate our discussion on the two major models proposed to date: interferometric quantum radar and quantum illumination. In addition, this book offers some new results, including an analytical study of quantum interferometry in the X-band radar region with a variety of atmospheric conditions, a derivation of a quantum radar equation, and a discussion of quantum radar jamming.This book assumes the reader is familiar w
Black hole spectroscopy from Loop Quantum Gravity models
Barrau, A.; Cao, Xiangyu; Noui, Karim; Perez, Alejandro
2015-01-01
Using Monte Carlo simulations, we compute the integrated emission spectra of black holes in the framework of Loop Quantum Gravity (LQG). The black hole emission rates are governed by the entropy whose value, in recent holographic loop quantum gravity models, was shown to agree at leading order with the Bekenstein-Hawking entropy. Quantum corrections depend on the Barbero-Immirzi parameter $\\gamma$. Starting with black holes of initial horizon area $A \\sim 10^2$ in Planck units, we present the...
Ruiz, Alfonso de la Fuente
2014-01-01
Brief description on the state of the art of some local optimization methods: Quantum annealing Quantum annealing (also known as alloy, crystallization or tempering) is analogous to simulated annealing but in substitution of thermal activation by quantum tunneling. The class of algorithmic methods for quantum annealing (dubbed: 'QA'), sometimes referred by the italian school as Quantum Stochastic Optimization ('QSO'), is a promising metaheuristic tool for solving local search problems in mult...
Haas, Fernando
2005-01-01
The quantum hydrodynamic model for charged particle systems is extended to the cases of non zero magnetic fields. In this way, quantum corrections to magnetohydrodynamics are obtained starting from the quantum hydrodynamical model with magnetic fields. The quantum magnetohydrodynamics model is analyzed in the infinite conductivity limit. The conditions for equilibrium in ideal quantum magnetohydrodynamics are established. Translationally invariant exact equilibrium solutions are obtained in t...
International Nuclear Information System (INIS)
Quantum ontologies are conceptions of the constitution of the universe that are compatible with quantum theory. The ontological orientation is contrasted to the pragmatic orientation of science, and reasons are given for considering quantum ontologies both within science, and in broader contexts. The principal quantum ontologies are described and evaluated. Invited paper at conference: Bell's Theorem, Quantum Theory, and Conceptions of the Universe, George Mason University, October 20-21, 1988. 16 refs
Scarani, Valerio; Iblisdir, Sofyan; Gisin, Nicolas; Acin, Antonio
2005-01-01
The impossibility of perfectly copying (or cloning) an arbitrary quantum state is one of the basic rules governing the physics of quantum systems. The processes that perform the optimal approximate cloning have been found in many cases. These "quantum cloning machines" are important tools for studying a wide variety of tasks, e.g. state estimation and eavesdropping on quantum cryptography. This paper provides a comprehensive review of quantum cloning machines (both for discrete-dimensional an...
Dotsenko, Igor; Mirrahimi, Mazyar; Brune, Michel; Haroche, Serge; Raimond, Jean-Michel; Rouchon, Pierre
2009-01-01
We propose a quantum feedback scheme for the preparation and protection of photon-number states of light trapped in a high-Q microwave cavity. A quantum nondemolition measurement of the cavity field provides information on the photon-number distribution. The feedback loop is closed by injecting into the cavity a coherent pulse adjusted to increase the probability of the target photon number. The efficiency and reliability of the closed-loop state stabilization is assessed by quantum Monte Car...
Effective Field Theory for Lattice Nuclei
Barnea, N.; Contessi, L.; Gazit, D.; Pederiva, F.; van Kolck, U.
2013-01-01
We show how nuclear effective field theory (EFT) and ab initio nuclear-structure methods can turn input from lattice quantum chromodynamics (LQCD) into predictions for the properties of nuclei. We argue that pionless EFT is the appropriate theory to describe the light nuclei obtained in recent LQCD simulations carried out at pion masses much heavier than the physical pion mass. We solve the EFT using the effective-interaction hyperspherical harmonics and auxiliary-field diffusion Monte Carlo ...
Quantum correlations; quantum probability approach
Majewski, W A
2014-01-01
This survey gives a comprehensive account of quantum correlations understood as a phenomenon stemming from the rules of quantization. Centered on quantum probability it describes the physical concepts related to correlations (both classical and quantum), mathematical structures, and their consequences. These include the canonical form of classical correlation functionals, general definitions of separable (entangled) states, definition and analysis of quantumness of correlations, description o...
Quantum Computer Games: Quantum Minesweeper
Gordon, Michal; Gordon, Goren
2010-01-01
The computer game of quantum minesweeper is introduced as a quantum extension of the well-known classical minesweeper. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. Quantum minesweeper demonstrates the effects of superposition, entanglement and their non-local characteristics. While in the classical…
Quantum CPU and Quantum Simulating
Wang, An Min
1999-01-01
Making use of an universal quantum network or QCPU proposed by me [6], some special quantum networks for simulating some quantum systems are given out. Specially, it is obtained that the quantum network for the time evolution operator which can simulate, in general, Schr\\"odinger equation.
Quantum CPU and Quantum Algorithm
Wang, An Min
1999-01-01
Making use of an universal quantum network -- QCPU proposed by me\\upcite{My1}, it is obtained that the whole quantum network which can implement some the known quantum algorithms including Deutsch algorithm, quantum Fourier transformation, Shor's algorithm and Grover's algorithm.
Quantum Entanglement and Quantum Chromodynamics
Abbas, Afsar
2000-01-01
Non-locality or entanglement is an experimentally well established property of quantum mechanics. Here we study the role of quantum entanglement for higher symmetry group like $ SU(3_c) $, the gauge group of quantum chromodynamics (QCD). We show that the hitherto unexplained property of confinement in QCD arises as a fundamental feature of quantum entanglement in $ SU(3_c) $.
Monte Carlo Particle Lists: MCPL
Kittelmann, Thomas; Knudsen, Erik B; Willendrup, Peter; Cai, Xiao Xiao; Kanaki, Kalliopi
2016-01-01
A binary format with lists of particle state information, for interchanging particles between various Monte Carlo simulation applications, is presented. Portable C code for file manipulation is made available to the scientific community, along with converters and plugins for several popular simulation packages.
Quantum teleportation and quantum information
International Nuclear Information System (INIS)
The scheme of quantum teleportation is described in a mathematically rigorous way, including analysis of the role and importance of quantum entanglement. The experiments with quantum teleportation performed in Innsbruck and in Rome are described in detail, and some differences between the two approaches are discussed. The elements of quantum information theory are introduced and compared with Shannon's classical information theory. The phenomenon of quantum teleportation is placed into a wider context of the developing quantum information theory, which enables quantum teleportation to be described by using the particle physics language. (Z.J.)
Quantum Correlations in Quantum Cloning
Chakrabarty, Indranil
2010-01-01
We utilize quantum discord to charecterize the correlation present in Buzek-Hillery quantum copying machine \\cite{bh} (not necessarily universal quantum cloning machine). In other words we quantify the correlation present beetween the original and the replicated copy of the quantum state obtained at the outport port, Interestingly, we find some domain of the machine parameter, for which the quantum disord is non negative even in the mere absence of entanglement. These non zero values of the quantum discord is a strong signature for the presence of non classical correlations. This is one step forward evidence in the support of the fact that quantum discord and entanglement are not synonymous.
Quantum noise and quantum communication
Jennewein, Thomas; Zeilinger, Anton
2004-05-01
We show how the probabilistic interpretation of quantum mechanics leads to unavoidable quantum noise, even for deterministic evolution of the quantum state. Far from being a nuisance, this consequent quantum randomness is at the heart of new concepts in technology. We discuss explicitly the quantum random number generator based on the partitition noise at the beam splitter. Another application of quantum noise is quantum cryptography, where the randomness of the detection event leads to the generation of a random cryptographic key at two locations without the necessity of transporting that key from A to B. Finally, we will show how quantum noise is an intrinsically important part of quantum teleportation, and we conclude with a brief discussion of the possibilities of free-space quantum communication.
Quantum Histories and Quantum Gravity
Henson, Joe
2009-01-01
This paper reviews the histories approach to quantum mechanics. This discussion is then applied to theories of quantum gravity. It is argued that some of the quantum histories must approximate (in a suitable sense) to classical histories, if the correct classical regime is to be recovered. This observation has significance for the formulation of new theories (such as quantum gravity theories) as it puts a constraint on the kinematics, if the quantum/classical correspondence principle is to be...
Quantum Monte Carlo Methods Describe Noncovalent Interactions with Subchemical Accuracy
Czech Academy of Sciences Publication Activity Database
Dubecký, M.; Jurečka, P.; Derian, R.; Hobza, Pavel; Otyepka, M.; Mitas, L.
2013-01-01
Roč. 9, č. 10 (2013), s. 4287-4292. ISSN 1549-9618 R&D Projects: GA ČR GBP208/12/G016 Grant ostatní: Operational Program Research and Development for Innovations(XE) CZ.1.05/2.1.00/03.0058; Operational Program Education for Competitiveness(XE) CZ.1.07/2.3.00/30.0004; Operational Program Education for Competitiveness(XE) CZ.1.07/2.3.00/20.0058 Institutional support: RVO:61388963 Keywords : Gaussian-basis sets * wave-functions * electronic-structure Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 5.310, year: 2013
Monte Carlo simulation of quantum mechanical many-body systems
International Nuclear Information System (INIS)
It is the aim of this thesis to calculate approximationless under given boundary conditions for the Schroedinger equation and symmetry conditions for the wave functions to calculate the ground state, i. e. the lowest eigenvalue and the corresponding wave function. (HSI)
Monte Carlo Simulation of stacked Quantum Dot Arrays
Kunert, Roland
2006-01-01
Die wissenschaftliche Untersuchung von Nanostrukturen gewann in den letzten Jahrzehnten in vielen Fachgebieten an immenser Bedeutung. Im Bereich der Festkörperphysik erwiesen sich insbesondere sogenannte Quantenpunkte, hergestellt aus halbleitenden Heterostrukturen, als Forschungsobjekte von herausragender Wichtigkeit. Die Eigenschaften von Quantenpunkten bieten ein breites Spektrum potenzieller Anwendungen und führten bereits jetzt zu neuen opto-elektronischen Bauteilen. Die mit diesem Theme...
Quantum Monte Carlo calculations of neutron-alpha scattering
Nollett, Kenneth M.; Pieper, Steven C.; Wiringa, R. B.; Carlson, J; Hale, G M
2006-01-01
We describe a new method to treat low-energy scattering problems in few-nucleon systems, and we apply it to the five-body case of neutron-alpha scattering. The method allows precise calculations of low-lying resonances and their widths. We find that a good three-nucleon interaction is crucial to obtain an accurate description of neutron-alpha scattering.
Pfeiffer, P.; Egusquiza, I. L.; Di Ventra, M.; Sanz, M.; Solano, E.
2016-01-01
Technology based on memristors, resistors with memory whose resistance depends on the history of the crossing charges, has lately enhanced the classical paradigm of computation with neuromorphic architectures. However, in contrast to the known quantized models of passive circuit elements, such as inductors, capacitors or resistors, the design and realization of a quantum memristor is still missing. Here, we introduce the concept of a quantum memristor as a quantum dissipative device, whose decoherence mechanism is controlled by a continuous-measurement feedback scheme, which accounts for the memory. Indeed, we provide numerical simulations showing that memory effects actually persist in the quantum regime. Our quantization method, specifically designed for superconducting circuits, may be extended to other quantum platforms, allowing for memristor-type constructions in different quantum technologies. The proposed quantum memristor is then a building block for neuromorphic quantum computation and quantum simulations of non-Markovian systems. PMID:27381511
Pfeiffer, P; Egusquiza, I L; Di Ventra, M; Sanz, M; Solano, E
2016-01-01
Technology based on memristors, resistors with memory whose resistance depends on the history of the crossing charges, has lately enhanced the classical paradigm of computation with neuromorphic architectures. However, in contrast to the known quantized models of passive circuit elements, such as inductors, capacitors or resistors, the design and realization of a quantum memristor is still missing. Here, we introduce the concept of a quantum memristor as a quantum dissipative device, whose decoherence mechanism is controlled by a continuous-measurement feedback scheme, which accounts for the memory. Indeed, we provide numerical simulations showing that memory effects actually persist in the quantum regime. Our quantization method, specifically designed for superconducting circuits, may be extended to other quantum platforms, allowing for memristor-type constructions in different quantum technologies. The proposed quantum memristor is then a building block for neuromorphic quantum computation and quantum simulations of non-Markovian systems. PMID:27381511
Boninsegni, M; Svistunov, B V
2006-01-01
A detailed description is provided of a new Worm Algorithm, enabling the accurate computation of thermodynamic properties of quantum many-body systems in continuous space, at finite temperature. The algorithm is formulated within the general Path Integral Monte Carlo (PIMC) scheme, but also allows one to perform quantum simulations in the grand canonical ensemble, as well as to compute off-diagonal imaginary-time correlation functions, such as the Matsubara Green function, simultaneously with diagonal observables. Another important innovation consists of the expansion of the attractive part of the pairwise potential energy into elementary (diagrammatic) contributions, which are then statistically sampled. This affords a complete microscopic account of the long-range part of the potential energy, while keeping the computational complexity of all updates independent of the size of the simulated system. The computational scheme allows for efficient calculations of the superfluid fraction and off-diagonal correla...
Chattaraj, Pratim Kumar
2010-01-01
The application of quantum mechanics to many-particle systems has been an active area of research in recent years as researchers have looked for ways to tackle difficult problems in this area. The quantum trajectory method provides an efficient computational technique for solving both stationary and time-evolving states, encompassing a large area of quantum mechanics. Quantum Trajectories brings the expertise of an international panel of experts who focus on the epistemological significance of quantum mechanics through the quantum theory of motion.Emphasizing a classical interpretation of quan
International Nuclear Information System (INIS)
A recently proposed test of quantumness Alicki and Van Ryn (2008 J. Phys. A: Math. Theor. 41 062001) is put into a broader mathematical and physical perspective. The notion of quantumness witnesses is introduced, in analogy to entanglement witnesses, and is illustrated by examples of single qubit and many-body systems with additive observables. We also compare our proposal with the quantumness test based on quantum correlations (entanglement) and Bell inequalities, and go on to discuss a class of quantumness witnesses associated with the phase-space representation of quantum mechanics
Entanglement negativity and conformal field theory: a Monte Carlo study
International Nuclear Information System (INIS)
We investigate the behavior of the moments of the partially transposed reduced density matrix ρAT2 in critical quantum spin chains. Given subsystem A as the union of two blocks, this is the (matrix) transpose of ρA with respect to the degrees of freedom of one of the two blocks. This is also the main ingredient for constructing the logarithmic negativity. We provide a new numerical scheme for efficiently calculating all the moments of ρAT2 using classical Monte Carlo simulations. In particular we study several combinations of the moments which are scale invariant at a critical point. Their behavior is fully characterized in both the critical Ising and the anisotropic Heisenberg XXZ chains. For two adjacent blocks we find, in both models, full agreement with recent conformal field theory (CFT) calculations. For disjoint blocks, in the Ising chain finite size corrections are nonnegligible. We demonstrate that their exponent is the same as that governing the unusual scaling corrections of the mutual information between the two blocks. Monte Carlo data fully match the theoretical CFT prediction only in the asymptotic limit of infinite intervals. Oppositely, in the Heisenberg chain scaling corrections are smaller and, already at finite (moderately large) block sizes, Monte Carlo data are in excellent agreement with the asymptotic CFT result. (paper)
Nonperturbative quantum de Sitter universe
International Nuclear Information System (INIS)
The dynamical generation of a four-dimensional classical universe from nothing but fundamental quantum excitations at the Planck scale is a long-standing challenge to theoretical physicists. A candidate theory of quantum gravity which achieves this goal without invoking exotic ingredients or excessive fine-tuning is based on the nonperturbative and background-independent technique of causal dynamical triangulations. We demonstrate in detail how in this approach a macroscopic de Sitter universe, accompanied by small quantum fluctuations, emerges from the full gravitational path integral, and how the effective action determining its dynamics can be reconstructed uniquely from Monte Carlo data. We also provide evidence that it may be possible to penetrate to the sub-Planckian regime, where the Planck length is large compared to the lattice spacing of the underlying regularization of geometry.
Deformations of quantum field theories and the construction of interacting models
International Nuclear Information System (INIS)
The subject of this thesis is the rigorous construction of quantum field theoretic models with nontrivial interaction. For this task techniques available in the framework of Algebraic Quantum Field Theory are applied and two different approaches are discussed. On the one hand, an inverse scattering problem is considered. A given scattering matrix is thereby taken as the starting point of the construction. In two spacetime dimensions one may work with factorizing scattering matrices which exhibit a simple structure. The particle spectrum taken into account involves an arbitrary number of massive particle species which transform under some global gauge group. It is a known fact that auxiliary fields with weakened localization, namely in wedges, can be constructed. In the main part of this thesis the more involved transition to local theories is shown by means of operator algebraic methods. Concretely, we make use of the so-called modular nuclearity condition. To this end, we investigate certain maps from the wedge algebras, generated by the auxiliary fields, to the considered Hilbert space. Under a very plausible conjecture it is shown that these maps are nuclear, which implies the nontriviality of algebras associated with bounded regions in the sense that the Reeh-Schlieder property holds. This construction method yields a large class of integrable models with factorizing S-matrices in two spacetime dimensions, complying with localization in bounded regions above a minimal size. The constructed family contains, for example, the multifaceted O(N)-invariant nonlinear sigma-models. On the other hand, deformation techniques constitute a method of construction which may be applied in arbitrary spacetime dimensions. This approach starts from a known quantum field theoretic model which is subjected to a certain modification. Here, concretely, the model of a scalar massive Fermion was deformed. It is shown that the correspondingly emerging models are based on fields with
Kinematics of multigrid Monte Carlo
International Nuclear Information System (INIS)
We study the kinematics of multigrid Monte Carlo algorithms by means of acceptance rates for nonlocal Metropolis update proposals. An approximation formula for acceptance rates is derived. We present a comparison of different coarse-to-fine interpolation schemes in free field theory, where the formula is exact. The predictions of the approximation formula for several interacting models are well confirmed by Monte Carlo simulations. The following rule is found: For a critical model with fundametal Hamiltonian Η(φ), absence of critical slowing down can only be expected if the expansion of (Η(φ+ψ)) in terms of the shift ψ contains no relevant (mass) term. We also introduce a multigrid update procedure for nonabelian lattice gauge theory and study the acceptance rates for gauge group SU(2) in four dimensions. (orig.)
Quantum robots and quantum computers
Energy Technology Data Exchange (ETDEWEB)
Benioff, P.
1998-07-01
Validation of a presumably universal theory, such as quantum mechanics, requires a quantum mechanical description of systems that carry out theoretical calculations and systems that carry out experiments. The description of quantum computers is under active development. No description of systems to carry out experiments has been given. A small step in this direction is taken here by giving a description of quantum robots as mobile systems with on board quantum computers that interact with different environments. Some properties of these systems are discussed. A specific model based on the literature descriptions of quantum Turing machines is presented.
Ground-state statistics from annealing algorithms: Quantum vs classical approaches
Matsuda, Yoshiki; Nishimori, Hidetoshi; Katzgraber, Helmut G.
2008-01-01
We study the performance of quantum annealing for systems with ground-state degeneracy by directly solving the Schr\\"odinger equation for small systems and quantum Monte Carlo simulations for larger systems. The results indicate that naive quantum annealing using a transverse field may not be well suited to identify all degenerate ground-state configurations, although the value of the ground-state energy is often efficiently estimated. An introduction of quantum transitions to all states with...
Putz, Volkmar
2015-01-01
We consider ways of conceptualizing, rendering and perceiving quantum music, and quantum art in general. Thereby we give particular emphasis to its non-classical aspects, such as coherent superposition and entanglement.
Energy Technology Data Exchange (ETDEWEB)
Zurek, Wojciech H [Los Alamos National Laboratory
2008-01-01
Quantum Darwinism - proliferation, in the environment, of multiple records of selected states of the system (its information-theoretic progeny) - explains how quantum fragility of individual state can lead to classical robustness of their multitude.
Valentini, Antony
2014-01-01
This paper collects into one place my replies to the questions posed by Maximilian Schlosshauer in his interview volume about the foundations of quantum mechanics, "Elegance and Enigma: The Quantum Interviews" (Springer, 2011).
Putz, Volkmar; Svozil, Karl
2015-01-01
We consider ways of conceptualizing, rendering and perceiving quantum music, and quantum art in general. Thereby, we give particular emphasis to its non-classical aspects, such as coherent superposition and entanglement.
Asynchronous Anytime Sequential Monte Carlo
Paige, Brooks; Wood, Frank; Doucet, Arnaud; Teh, Yee Whye
2014-01-01
We introduce a new sequential Monte Carlo algorithm we call the particle cascade. The particle cascade is an asynchronous, anytime alternative to traditional particle filtering algorithms. It uses no barrier synchronizations which leads to improved particle throughput and memory efficiency. It is an anytime algorithm in the sense that it can be run forever to emit an unbounded number of particles while keeping within a fixed memory budget. We prove that the particle cascade is an unbiased mar...
Neural Adaptive Sequential Monte Carlo
Gu, Shixiang; Ghahramani, Zoubin; Turner, Richard E
2015-01-01
Sequential Monte Carlo (SMC), or particle filtering, is a popular class of methods for sampling from an intractable target distribution using a sequence of simpler intermediate distributions. Like other importance sampling-based methods, performance is critically dependent on the proposal distribution: a bad proposal can lead to arbitrarily inaccurate estimates of the target distribution. This paper presents a new method for automatically adapting the proposal using an approximation of the Ku...
Parallel Monte Carlo reactor neutronics
International Nuclear Information System (INIS)
The issues affecting implementation of parallel algorithms for large-scale engineering Monte Carlo neutron transport simulations are discussed. For nuclear reactor calculations, these include load balancing, recoding effort, reproducibility, domain decomposition techniques, I/O minimization, and strategies for different parallel architectures. Two codes were parallelized and tested for performance. The architectures employed include SIMD, MIMD-distributed memory, and workstation network with uneven interactive load. Speedups linear with the number of nodes were achieved
Adaptive Multilevel Monte Carlo Simulation
Hoel, H
2011-08-23
This work generalizes a multilevel forward Euler Monte Carlo method introduced in Michael B. Giles. (Michael Giles. Oper. Res. 56(3):607–617, 2008.) for the approximation of expected values depending on the solution to an Itô stochastic differential equation. The work (Michael Giles. Oper. Res. 56(3):607– 617, 2008.) proposed and analyzed a forward Euler multilevelMonte Carlo method based on a hierarchy of uniform time discretizations and control variates to reduce the computational effort required by a standard, single level, Forward Euler Monte Carlo method. This work introduces an adaptive hierarchy of non uniform time discretizations, generated by an adaptive algorithmintroduced in (AnnaDzougoutov et al. Raùl Tempone. Adaptive Monte Carlo algorithms for stopped diffusion. In Multiscale methods in science and engineering, volume 44 of Lect. Notes Comput. Sci. Eng., pages 59–88. Springer, Berlin, 2005; Kyoung-Sook Moon et al. Stoch. Anal. Appl. 23(3):511–558, 2005; Kyoung-Sook Moon et al. An adaptive algorithm for ordinary, stochastic and partial differential equations. In Recent advances in adaptive computation, volume 383 of Contemp. Math., pages 325–343. Amer. Math. Soc., Providence, RI, 2005.). This form of the adaptive algorithm generates stochastic, path dependent, time steps and is based on a posteriori error expansions first developed in (Anders Szepessy et al. Comm. Pure Appl. Math. 54(10):1169– 1214, 2001). Our numerical results for a stopped diffusion problem, exhibit savings in the computational cost to achieve an accuracy of ϑ(TOL),from(TOL−3), from using a single level version of the adaptive algorithm to ϑ(((TOL−1)log(TOL))2).
Monomial Gamma Monte Carlo Sampling
Zhang, Yizhe; Wang, Xiangyu; Chen, Changyou; Fan, Kai; Carin, Lawrence
2016-01-01
We unify slice sampling and Hamiltonian Monte Carlo (HMC) sampling by demonstrating their connection under the canonical transformation from Hamiltonian mechanics. This insight enables us to extend HMC and slice sampling to a broader family of samplers, called monomial Gamma samplers (MGS). We analyze theoretically the mixing performance of such samplers by proving that the MGS draws samples from a target distribution with zero-autocorrelation, in the limit of a single parameter. This propert...
Extending canonical Monte Carlo methods
Velazquez, L.; Curilef, S.
2010-02-01
In this paper, we discuss the implications of a recently obtained equilibrium fluctuation-dissipation relation for the extension of the available Monte Carlo methods on the basis of the consideration of the Gibbs canonical ensemble to account for the existence of an anomalous regime with negative heat capacities C < 0. The resulting framework appears to be a suitable generalization of the methodology associated with the so-called dynamical ensemble, which is applied to the extension of two well-known Monte Carlo methods: the Metropolis importance sampling and the Swendsen-Wang cluster algorithm. These Monte Carlo algorithms are employed to study the anomalous thermodynamic behavior of the Potts models with many spin states q defined on a d-dimensional hypercubic lattice with periodic boundary conditions, which successfully reduce the exponential divergence of the decorrelation time τ with increase of the system size N to a weak power-law divergence \\tau \\propto N^{\\alpha } with α≈0.2 for the particular case of the 2D ten-state Potts model.
International Nuclear Information System (INIS)
We have shown that the transport equation can be solved with particles, like the Monte-Carlo method, but without random numbers. In the Monte-Carlo method, particles are created from the source, and are followed from collision to collision until either they are absorbed or they leave the spatial domain. In our method, particles are created from the original source, with a variable weight taking into account both collision and absorption. These particles are followed until they leave the spatial domain, and we use them to determine a first collision source. Another set of particles is then created from this first collision source, and tracked to determine a second collision source, and so on. This process introduces an approximation which does not exist in the Monte-Carlo method. However, we have analyzed the effect of this approximation, and shown that it can be limited. Our method is deterministic, gives reproducible results. Furthermore, when extra accuracy is needed in some region, it is easier to get more particles to go there. It has the same kind of applications: rather problems where streaming is dominant than collision dominated problems
Ionescu, Lucian M
2010-01-01
Quantum Relativity is supposed to be a new theory, which locally is a deformation of Special Relativity, and globally it is a background independent theory including the main ideas of General Relativity, with hindsight from Quantum Theory. The qubit viewed as a Hopf monopole bundle is considered as a unifying gauge "group". Breaking its chiral symmetry is conjectured to yield gravity as a deformation of electromagnetism. It is already a quantum theory in the context of Quantum Information Dyn...
Eisert, J
2000-01-01
In these lecture notes we investigate the implications of the identification of strategies with quantum operations in game theory beyond the results presented in [J. Eisert, M. Wilkens, and M. Lewenstein, Phys. Rev. Lett. 83, 3077 (1999)]. After introducing a general framework, we study quantum games with a classical analogue in order to flesh out the peculiarities of game theoretical settings in the quantum domain. Special emphasis is given to a detailed investigation of different sets of quantum strategies.
Singh, Sudhir Kumar; Srikanth, R.
2004-01-01
A quantum seal is a way of encoding a message into quantum states, so that anybody may read the message with little error, while authorized verifiers can detect that the seal has been broken. We present a simple extension to the Bechmann-Pasquinucci majority-voting scheme that is impervious to coherent attacks, and further, encompasses sealing quantum messages by means of quantum encryption. The scheme is relatively easy to implement, requiring neither entanglement nor controlled operations d...
Slavnov, D. A.
2009-01-01
In the framework of an algebraic approach, we consider a quantum teleportation procedure. It turns out that using the quantum measurement nonlocality hypothesis is unnecessary for describing this procedure. We study the question of what material objects are information carriers for quantum teleportation.
Coleman, P.; Schofield, A.J.
2005-01-01
As we mark the centenary of Albert Einstein's seminal contribution to both quantum mechanics and special relativity, we approach another anniversary--that of Einstein's foundation of the quantum theory of solids. But 100 years on, the same experimental measurement that puzzled Einstein and his contemporaries is forcing us to question our understanding of how quantum matter transforms at ultra-low temperatures.
I, Quantum Robot: Quantum Mind control on a Quantum Computer
Zizzi, Paola
2008-01-01
The logic which describes quantum robots is not orthodox quantum logic, but a deductive calculus which reproduces the quantum tasks (computational processes, and actions) taking into account quantum superposition and quantum entanglement. A way toward the realization of intelligent quantum robots is to adopt a quantum metalanguage to control quantum robots. A physical implementation of a quantum metalanguage might be the use of coherent states in brain signals.
Quantum Logic and Quantum Computation
Pavicic, Mladen; Megill, Norman D.
2008-01-01
We use classes of Hilbert lattice equations for an alternative representation of Hilbert lattices and Hilbert spaces of arbitrary quantum systems that might enable a direct introduction of the states of the systems into quantum computers. More specifically, we look for a way to feed a quantum computer with algebraic equations of n-th order underlying an infinite dimensional Hilbert space description of quantum systems. A number of new results on states defined on Hilbert lattices are presente...
Moulick, Subhayan Roy; Panigrahi, Prasanta K.
2016-06-01
We propose the idea of a quantum cheque scheme, a cryptographic protocol in which any legitimate client of a trusted bank can issue a cheque, that cannot be counterfeited or altered in anyway, and can be verified by a bank or any of its branches. We formally define a quantum cheque and present the first unconditionally secure quantum cheque scheme and show it to be secure against any no-signalling adversary. The proposed quantum cheque scheme can been perceived as the quantum analog of Electronic Data Interchange, as an alternate for current e-Payment Gateways.
Quantum entanglement and quantum operation
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
It is a simple introduction to quantum entanglement and quantum operations. The authors focus on some applications of quantum entanglement and relations between two-qubit entangled states and unitary operations. It includes remote state preparation by using any pure entangled states, nonlocal operation implementation using entangled states, entanglement capacity of two-qubit gates and two-qubit gates construction.
Yang, S. -R. Eric; Schliemann, John; MacDonald, A. H.
2002-01-01
Bilayer quantum Hall systems can form collective states in which electrons exhibit spontaneous interlayer phase coherence. We discuss the possibility of using bilayer quantum dot many-electron states with this property to create two-level systems that have potential advantages as quantum bits.
Algorithm for Computing Excited States in Quantum Theory
Luo, X. Q.; Jirari, H.; Kroger, H; Moriarty, K.
2001-01-01
Monte Carlo techniques have been widely employed in statistical physics as well as in quantum theory in the Lagrangian formulation. However, in the conventional approach, it is extremely difficult to compute the excited states. Here we present a different algorithm: the Monte Carlo Hamiltonian method, designed to overcome the difficulties of the conventional approach. As a new example, application to the Klein-Gordon field theory is shown.
Quantum narrowing effect in a spin-Peierls system with quantum lattice fluctuation
International Nuclear Information System (INIS)
We investigate a one-dimensional S=1/2 antiferromagnetic Heisenberg model coupled to quantum lattice vibration using a quantum Monte Carlo method. We study the ground-state lattice fluctuation where the system shows a characteristic structure factor. We also study the mass dependence of magnetic properties such as the magnetic susceptibility and the magnetic excitation spectrum. For heavy mass, the system shows the same behavior as the case of classical lattice vibration. On the other hand, for light mass, magnetic properties coincide with those of the static uniform chain. We investigate the physical mechanism of this behavior and propose the picture of quantum narrowing. (author)
Construction of spin models displaying quantum criticality from quantum field theory
International Nuclear Information System (INIS)
We provide a method for constructing finite temperature states of one-dimensional spin chains displaying quantum criticality. These models are constructed using correlators of products of quantum fields and have an analytical purification. Their properties can be investigated by Monte Carlo simulations, which enable us to study the low-temperature phase diagram and to show that it displays a region of quantum criticality. The mixed states obtained are shown to be close to the thermal state of a simple nearest neighbor Hamiltonian
Quantum information. Teleporation - cryptography - quantum computer
International Nuclear Information System (INIS)
The following topics are dealt with: Reality in the test house, quantum teleportation, 100 years of quantum theory, the reality of quanta, interactionless quantum measurement, rules for quantum computers, quantum computers with ions, spintronics with diamond, the limits of the quantum computers, a view into the future of quantum optics. (HSI)
Quantum Games and Quantum Discord
Nawaz, Ahmad
2010-01-01
We quantize prisoners dilemma and chicken game by our generalized quantization scheme to explore the role of quantum discord in quantum games. In order to establish this connection we use Werner-like state as an initial state of the game. In this quantization scheme measurement can be performed in entangled as well as in product basis. For the measurement in entangled basis the dilemma in both the games can be resolved by separable states with non-zero quantum discord. Similarly for product basis measurement the payoffs are quantum mechanical only for nonzero values of quantum discord.
Forward physics Monte Carlo (FPMC)
Czech Academy of Sciences Publication Activity Database
Boonekamp, M.; Juránek, Vojtěch; Kepka, Oldřich; Royon, C.
Hamburg : Verlag Deutsches Elektronen-Synchrotron, 2009 - (Jung, H.; De Roeck, A.), s. 758-762 ISBN N. [HERA and the LHC workshop series on the implications of HERA for LHC physics. Geneve (CH), 26.05.2008-30.05.2008] R&D Projects: GA MŠk LC527; GA MŠk LA08032 Institutional research plan: CEZ:AV0Z10100502 Keywords : forward physics * diffraction * two-photon * Monte Carlo Subject RIV: BF - Elementary Particles and High Energy Physics http://arxiv.org/PS_cache/arxiv/pdf/0903/0903.3861v2.pdf
Monte Carlo techniques in radiation therapy
Verhaegen, Frank
2013-01-01
Modern cancer treatment relies on Monte Carlo simulations to help radiotherapists and clinical physicists better understand and compute radiation dose from imaging devices as well as exploit four-dimensional imaging data. With Monte Carlo-based treatment planning tools now available from commercial vendors, a complete transition to Monte Carlo-based dose calculation methods in radiotherapy could likely take place in the next decade. Monte Carlo Techniques in Radiation Therapy explores the use of Monte Carlo methods for modeling various features of internal and external radiation sources, including light ion beams. The book-the first of its kind-addresses applications of the Monte Carlo particle transport simulation technique in radiation therapy, mainly focusing on external beam radiotherapy and brachytherapy. It presents the mathematical and technical aspects of the methods in particle transport simulations. The book also discusses the modeling of medical linacs and other irradiation devices; issues specific...
Monte Carlo primer for health physicists
International Nuclear Information System (INIS)
The basic ideas and principles of Monte Carlo calculations are presented in the form of a primer for health physicists. A simple integral with a known answer is evaluated by two different Monte Carlo approaches. Random number, which underlie Monte Carlo work, are discussed, and a sample table of random numbers generated by a hand calculator is presented. Monte Carlo calculations of dose and linear energy transfer (LET) from 100-keV neutrons incident on a tissue slab are discussed. The random-number table is used in a hand calculation of the initial sequence of events for a 100-keV neutron entering the slab. Some pitfalls in Monte Carlo work are described. While this primer addresses mainly the bare bones of Monte Carlo, a final section briefly describes some of the more sophisticated techniques used in practice to reduce variance and computing time
Ryabov, V. A.
2015-08-01
Quantum systems in a mechanical embedding, the breathing mode of a small particles, optomechanical system, etc. are far not the full list of examples in which the volume exhibits quantum behavior. Traditional consideration suggests strain in small systems as a result of a collective movement of particles, rather than the dynamics of the volume as an independent variable. The aim of this work is to show that some problem here might be essentially simplified by introducing periodic boundary conditions. At this case, the volume is considered as the independent dynamical variable driven by the internal pressure. For this purpose, the concept of quantum volume based on Schrödinger’s equation in 𝕋3 manifold is proposed. It is used to explore several 1D model systems: An ensemble of free particles under external pressure, quantum manometer and a quantum breathing mode. In particular, the influence of the pressure of free particle on quantum oscillator is determined. It is shown also that correction to the spectrum of the breathing mode due to internal degrees of freedom is determined by the off-diagonal matrix elements of the quantum stress. The new treatment not using the “force” theorem is proposed for the quantum stress tensor. In the general case of flexible quantum 3D dynamics, quantum deformations of different type might be introduced similarly to monopole mode.
Non-periodic pseudo-random numbers used in Monte Carlo calculations
International Nuclear Information System (INIS)
The generation of pseudo-random numbers is one of the interesting problems in Monte Carlo simulations, mostly because the common computer generators produce periodic numbers. We used simple pseudo-random numbers generated with the simplest chaotic system, the logistic map, with excellent results. The numbers generated in this way are non-periodic, which we demonstrated for 1013 numbers, and they are obtained in a deterministic way, which allows to repeat systematically any calculation. The Monte Carlo calculations are the ideal field to apply these numbers, and we did it for simple and more elaborated cases. Chemistry and Information Technology use this kind of simulations, and the application of this numbers to quantum Monte Carlo and cryptography is immediate. I present here the techniques to calculate, analyze and use these pseudo-random numbers, show that they lack periodicity up to 1013 numbers and that they are not correlated
A first look at Quasi-Monte Carlo for lattice field theory problems
Energy Technology Data Exchange (ETDEWEB)
Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Leovey, H.; Griewank, A. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Mathematik; Nube, A. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Mueller-Preussker, M. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik
2012-11-15
In this project we initiate an investigation of the applicability of Quasi-Monte Carlo methods to lattice field theories in order to improve the asymptotic error behavior of observables for such theories. In most cases the error of an observable calculated by averaging over random observations generated from an ordinary Monte Carlo simulation behaves like N{sup -1/2}, where N is the number of observations. By means of Quasi-Monte Carlo methods it is possible to improve this behavior for certain problems to up to N{sup -1}. We adapted and applied this approach to simple systems like the quantum harmonic and anharmonic oscillator and verified an improved error scaling.
Interacting Particle Markov Chain Monte Carlo
Rainforth, Tom; Naesseth, Christian A.; Lindsten, Fredrik; Paige, Brooks; van de Meent, Jan-Willem; Doucet, Arnaud; Wood, Frank
2016-01-01
We introduce interacting particle Markov chain Monte Carlo (iPMCMC), a PMCMC method that introduces a coupling between multiple standard and conditional sequential Monte Carlo samplers. Like related methods, iPMCMC is a Markov chain Monte Carlo sampler on an extended space. We present empirical results that show significant improvements in mixing rates relative to both non-interacting PMCMC samplers and a single PMCMC sampler with an equivalent total computational budget. An additional advant...
Microcomputer quantum mechanics
International Nuclear Information System (INIS)
Chapter headings are: microcomputers and BASIC; tuning the instrument; the iterative approach; some finite-difference methods; numerical integration; Pade approximants and all that; a simple power series method; some matrix calculations; hypervirial-perturbation methods; finite-difference eigenvalue calculations; one-dimensional model problems; some case studies (a simple helium atom calculation; Monte-Carlo optimization; the charmonium problem; the quadratic Zeeman effect; quasi-bound states). While the first chapters deal with general ways of applying and testing microcomputers the later chapters concentrate on the use of microcomputers in quantum mechanics. Worked exercises are given in the text and provide concrete uses for the computing skills that are discussed. (U.K.)
1-D EQUILIBRIUM DISCRETE DIFFUSION MONTE CARLO
Energy Technology Data Exchange (ETDEWEB)
T. EVANS; ET AL
2000-08-01
We present a new hybrid Monte Carlo method for 1-D equilibrium diffusion problems in which the radiation field coexists with matter in local thermodynamic equilibrium. This method, the Equilibrium Discrete Diffusion Monte Carlo (EqDDMC) method, combines Monte Carlo particles with spatially discrete diffusion solutions. We verify the EqDDMC method with computational results from three slab problems. The EqDDMC method represents an incremental step toward applying this hybrid methodology to non-equilibrium diffusion, where it could be simultaneously coupled to Monte Carlo transport.
Monte Carlo Application ToolKit (MCATK)
International Nuclear Information System (INIS)
Highlights: • Component-based Monte Carlo radiation transport parallel software library. • Designed to build specialized software applications. • Provides new functionality for existing general purpose Monte Carlo transport codes. • Time-independent and time-dependent algorithms with population control. • Algorithm verification and validation results are provided. - Abstract: The Monte Carlo Application ToolKit (MCATK) is a component-based software library designed to build specialized applications and to provide new functionality for existing general purpose Monte Carlo radiation transport codes. We will describe MCATK and its capabilities along with presenting some verification and validations results
Multidimensional stochastic approximation Monte Carlo.
Zablotskiy, Sergey V; Ivanov, Victor A; Paul, Wolfgang
2016-06-01
Stochastic Approximation Monte Carlo (SAMC) has been established as a mathematically founded powerful flat-histogram Monte Carlo method, used to determine the density of states, g(E), of a model system. We show here how it can be generalized for the determination of multidimensional probability distributions (or equivalently densities of states) of macroscopic or mesoscopic variables defined on the space of microstates of a statistical mechanical system. This establishes this method as a systematic way for coarse graining a model system, or, in other words, for performing a renormalization group step on a model. We discuss the formulation of the Kadanoff block spin transformation and the coarse-graining procedure for polymer models in this language. We also apply it to a standard case in the literature of two-dimensional densities of states, where two competing energetic effects are present g(E_{1},E_{2}). We show when and why care has to be exercised when obtaining the microcanonical density of states g(E_{1}+E_{2}) from g(E_{1},E_{2}). PMID:27415383
Single scatter electron Monte Carlo
Energy Technology Data Exchange (ETDEWEB)
Svatos, M.M. [Lawrence Livermore National Lab., CA (United States)|Wisconsin Univ., Madison, WI (United States)
1997-03-01
A single scatter electron Monte Carlo code (SSMC), CREEP, has been written which bridges the gap between existing transport methods and modeling real physical processes. CREEP simulates ionization, elastic and bremsstrahlung events individually. Excitation events are treated with an excitation-only stopping power. The detailed nature of these simulations allows for calculation of backscatter and transmission coefficients, backscattered energy spectra, stopping powers, energy deposits, depth dose, and a variety of other associated quantities. Although computationally intense, the code relies on relatively few mathematical assumptions, unlike other charged particle Monte Carlo methods such as the commonly-used condensed history method. CREEP relies on sampling the Lawrence Livermore Evaluated Electron Data Library (EEDL) which has data for all elements with an atomic number between 1 and 100, over an energy range from approximately several eV (or the binding energy of the material) to 100 GeV. Compounds and mixtures may also be used by combining the appropriate element data via Bragg additivity.
Levy, Amikam; Diósi, Lajos; Kosloff, Ronnie
2016-05-01
In this work we present the concept of a quantum flywheel coupled to a quantum heat engine. The flywheel stores useful work in its energy levels, while additional power is extracted continuously from the device. Generally, the energy exchange between a quantum engine and a quantized work repository is accompanied by heat, which degrades the charging efficiency. Specifically when the quantum harmonic oscillator acts as a work repository, quantum and thermal fluctuations dominate the dynamics. Quantum monitoring and feedback control are applied to the flywheel in order to reach steady state and regulate its operation. To maximize the charging efficiency one needs a balance between the information gained by measuring the system and the information fed back to the system. The dynamics of the flywheel are described by a stochastic master equation that accounts for the engine, the external driving, the measurement, and the feedback operations.
Busch, Paul; Pellonpää, Juha-Pekka; Ylinen, Kari
2016-01-01
This is a book about the Hilbert space formulation of quantum mechanics and its measurement theory. It contains a synopsis of what became of the Mathematical Foundations of Quantum Mechanics since von Neumann’s classic treatise with this title. Fundamental non-classical features of quantum mechanics—indeterminacy and incompatibility of observables, unavoidable measurement disturbance, entanglement, nonlocality—are explicated and analysed using the tools of operational quantum theory. The book is divided into four parts: 1. Mathematics provides a systematic exposition of the Hilbert space and operator theoretic tools and relevant measure and integration theory leading to the Naimark and Stinespring dilation theorems; 2. Elements develops the basic concepts of quantum mechanics and measurement theory with a focus on the notion of approximate joint measurability; 3. Realisations offers in-depth studies of the fundamental observables of quantum mechanics and some of their measurement implementations; and 4....
Scheck, Florian
2013-01-01
Scheck’s Quantum Physics presents a comprehensive introductory treatment, ideally suited for a two-semester course. Part One covers the basic principles and prime applications of quantum mechanics, from the uncertainty relations to many-body systems. Part Two introduces to relativistic quantum field theory and ranges from symmetries in quantum physics to electroweak interactions. Numerous worked-out examples as well as exercises, with solutions or hints, enables the book’s use as an accompanying text for courses, and also for independent study. For both parts, the necessary mathematical framework is treated in adequate form and detail. The book ends with appendices covering mathematical fundamentals and enrichment topics, plus selected biographical notes on pioneers of quantum mechanics and quantum field theory. The new edition was thoroughly revised and now includes new sections on quantization using the path integral method and on deriving generalized path integrals for bosonic and fermionic fields.
International Nuclear Information System (INIS)
This book discusses the state of the art of quantum gravity, quantum effects in cosmology, quantum black-hole physics, recent developments in supergravity, and quantum gauge theories. Topics considered include the problems of general relativity, pregeometry, complete cosmological theories, quantum fluctuations in cosmology and galaxy formation, a new inflationary universe scenario, grand unified phase transitions and the early Universe, the generalized second law of thermodynamics, vacuum polarization near black holes, the relativity of vacuum, black hole evaporations and their cosmological consequences, currents in supersymmetric theories, the Kaluza-Klein theories, gauge algebra and quantization, and twistor theory. This volume constitutes the proceedings of the Second Seminar on Quantum Gravity held in Moscow in 1981
Monte Carlo Studies of particle dffusion on a patchwise bivariate surface
Czech Academy of Sciences Publication Activity Database
Tarasenko, Alexander; Jastrabík, Lubomír
Barcelona : ThinkMind IARIA, 2013 - (Priviman, V.; Ovchinnikov, V.), s. 7-12 ISBN 9781629930640. [ International Conference on Quantum, Nano and Micro Technologies /7./ ICQNM 2013. Barcelona (ES), 25.08.2013-31.08.2013] R&D Projects: GA TA ČR TA01010517; GA ČR GAP108/12/1941 Institutional support: RVO:68378271 Keywords : surface diffusion * kinetic Monte Carlo simulations * patchwise lattice Subject RIV: BM - Solid Matter Physics ; Magnetism
A configuration space Monte Carlo algorithm for solving the nuclear pairing problem
Lingle, Mark
Nuclear pairing correlations using Quantum Monte Carlo are studied in this dissertation. We start by defining the nuclear pairing problem and discussing several historical methods developed to solve this problem, paying special attention to the applicability of such methods. A numerical example discussing pairing correlations in several calcium isotopes using the BCS and Exact Pairing solutions are presented. The ground state energies, correlation energies, and occupation numbers are compared to determine the applicability of each approach to realistic cases. Next we discuss some generalities related to the theory of Markov Chains and Quantum Monte Carlo in regards to nuclear structure. Finally we present our configuration space Monte Carlo algorithm starting from a discussion of a path integral approach by the authors. Some general features of the Pairing Hamiltonian that boost the effectiveness of a configuration space Monte Carlo approach are mentioned. The full details of our method are presented and special attention is paid to convergence and error control. We present a series of examples illustrating the effectiveness of our approach. These include situations with non-constant pairing strengths, limits when pairing correlations are weak, the computation of excited states, and problems when the relevant configuration space is large. We conclude with a chapter examining some of the effects of continuum states in 24O.
Fateev, Evgeny G.
2013-01-01
The principles of quantum motors based on Casimir platforms (thin-film nanostructures are at issue) are discussed in plain language. The generation of quantum propulsion is caused by the noncompensated integral action of virtual photon momenta upon a configuration unit cell in the platform. The cells in a Casimir platform should be situated in a certain order with optimal geometric parameters. The evaluation of the quantum propulsion shows that, for example, ten square meters of ideal Casimir...
Hughes, Richard J.; Alde, D. M.; Dyer, P.; Luther, G. G.; Morgan, G. L.; Schauer, M
1995-01-01
Quantum cryptography is a new method for secret communications offering the ultimate security assurance of the inviolability of a Law of Nature. In this paper we shall describe the theory of quantum cryptography, its potential relevance and the development of a prototype system at Los Alamos, which utilises the phenomenon of single-photon interference to perform quantum cryptography over an optical fiber communications link.
Barnett, Stephen M
2009-01-01
Quantum information- the subject- is a new and exciting area of science, which brings together physics, information theory, computer science and mathematics. "Quantum Information"- the book- is based on two successful lecture courses given to advanced undergraduate and beginning postgraduate students in physics. The intention is to introduce readers at this level to the fundamental, but offer rather simple, ideas behind ground-breaking developments including quantum cryptography,teleportation and quantum computing. The text is necessarily rather mathematical in style, but the mathema
International Nuclear Information System (INIS)
There is more to information than a string of ones and zeroes the ability of ''quantum bits'' to be in two states at the same time could revolutionize information technology. In the mid-1930s two influential but seemingly unrelated papers were published. In 1935 Einstein, Podolsky and Rosen proposed the famous EPR paradox that has come to symbolize the mysteries of quantum mechanics. Two years later, Alan Turing introduced the universal Turing machine in an enigmatically titled paper, On computable numbers, and laid the foundations of the computer industry one of the biggest industries in the world today. Although quantum physics is essential to understand the operation of transistors and other solid-state devices in computers, computation itself has remained a resolutely classical process. Indeed it seems only natural that computation and quantum theory should be kept as far apart as possible surely the uncertainty associated with quantum theory is anathema to the reliability expected from computers? Wrong. In 1985 David Deutsch introduced the universal quantum computer and showed that quantum theory can actually allow computers to do more rather than less. The ability of particles to be in a superposition of more than one quantum state naturally introduces a form of parallelism that can, in principle, perform some traditional computing tasks faster than is possible with classical computers. Moreover, quantum computers are capable of other tasks that are not conceivable with their classical counterparts. Similar breakthroughs in cryptography and communication followed. (author)
Quantum Networks for Generating Arbitrary Quantum States
Kaye, Phillip; Mosca, Michele
2004-01-01
Quantum protocols often require the generation of specific quantum states. We describe a quantum algorithm for generating any prescribed quantum state. For an important subclass of states, including pure symmetric states, this algorithm is efficient.
Dissipative quantum computing with open quantum walks
Energy Technology Data Exchange (ETDEWEB)
Sinayskiy, Ilya; Petruccione, Francesco [National Institute for Theoretical Physics and Quantum Research Group, School of Chemistry and Physics, University of KwaZulu-Natal, Durban (South Africa)
2014-12-04
An open quantum walk approach to the implementation of a dissipative quantum computing scheme is presented. The formalism is demonstrated for the example of an open quantum walk implementation of a 3 qubit quantum circuit consisting of 10 gates.
Quantum information and computation
Bub, Jeffrey
2005-01-01
This article deals with theoretical developments in the subject of quantum information and quantum computation, and includes an overview of classical information and some relevant quantum mechanics. The discussion covers topics in quantum communication, quantum cryptography, and quantum computation, and concludes by considering whether a perspective in terms of quantum information sheds new light on the conceptual problems of quantum mechanics.
Quantum physics without quantum philosophy
International Nuclear Information System (INIS)
Integrates and comments on the authors' seminal papers in the field. Emphasizes the natural way in which quantum phenomena emerge from the Bohmian picture. Helps to answer many of the objections raised to Bohmian quantum mechanics. Useful overview and summary for newcomers and students. It has often been claimed that without drastic conceptual innovations a genuine explanation of quantum interference effects and quantum randomness is impossible. This book concerns Bohmian mechanics, a simple particle theory that is a counterexample to such claims. The gentle introduction and other contributions collected here show how the phenomena of non-relativistic quantum mechanics, from Heisenberg's uncertainty principle to non-commuting observables, emerge from the Bohmian motion of particles, the natural particle motion associated with Schroedinger's equation. This book will be of value to all students and researchers in physics with an interest in the meaning of quantum theory as well as to philosophers of science.
Quantum physics without quantum philosophy
Energy Technology Data Exchange (ETDEWEB)
Duerr, Detlef [Muenchen Univ. (Germany). Mathematisches Inst.; Goldstein, Sheldon [Rutgers State Univ., Piscataway, NJ (United States). Dept. of Mathematics; Zanghi, Nino [Genova Univ. (Italy); Istituto Nazionale Fisica Nucleare, Genova (Italy)
2013-02-01
Integrates and comments on the authors' seminal papers in the field. Emphasizes the natural way in which quantum phenomena emerge from the Bohmian picture. Helps to answer many of the objections raised to Bohmian quantum mechanics. Useful overview and summary for newcomers and students. It has often been claimed that without drastic conceptual innovations a genuine explanation of quantum interference effects and quantum randomness is impossible. This book concerns Bohmian mechanics, a simple particle theory that is a counterexample to such claims. The gentle introduction and other contributions collected here show how the phenomena of non-relativistic quantum mechanics, from Heisenberg's uncertainty principle to non-commuting observables, emerge from the Bohmian motion of particles, the natural particle motion associated with Schroedinger's equation. This book will be of value to all students and researchers in physics with an interest in the meaning of quantum theory as well as to philosophers of science.
Simulated annealing versus quantum annealing
Troyer, Matthias
Based on simulated classical annealing and simulated quantum annealing using quantum Monte Carlo (QMC) simulations I will explore the question where physical or simulated quantum annealers may outperform classical optimization algorithms. Although the stochastic dynamics of QMC simulations is not the same as the unitary dynamics of a quantum system, I will first show that for the problem of quantum tunneling between two local minima both QMC simulations and a physical system exhibit the same scaling of tunneling times with barrier height. The scaling in both cases is O (Δ2) , where Δ is the tunneling splitting. An important consequence is that QMC simulations can be used to predict the performance of a quantum annealer for tunneling through a barrier. Furthermore, by using open instead of periodic boundary conditions in imaginary time, equivalent to a projector QMC algorithm, one obtains a quadratic speedup for QMC, and achieve linear scaling in Δ. I will then address the apparent contradiction between experiments on a D-Wave 2 system that failed to see evidence of quantum speedup and previous QMC results that indicated an advantage of quantum annealing over classical annealing for spin glasses. We find that this contradiction is resolved by taking the continuous time limit in the QMC simulations which then agree with the experimentally observed behavior and show no speedup for 2D spin glasses. However, QMC simulations with large time steps gain further advantage: they ``cheat'' by ignoring what happens during a (large) time step, and can thus outperform both simulated quantum annealers and classical annealers. I will then address the question how to optimally run a simulated or physical quantum annealer. Investigating the behavior of the tails of the distribution of runtimes for very hard instances we find that adiabatically slow annealing is far from optimal. On the contrary, many repeated relatively fast annealing runs can be orders of magnitude faster for
Quantum Schubert polynomials and quantum Schur functions
Kirillov, Anatol N.
1997-01-01
We introduce the quantum multi-Schur functions, quantum factorial Schur functions and quantum Macdonald polynomials. We prove that for restricted vexillary permutations the quantum double Schubert polynomial coincides with some quantum multi-Schur function and prove a quantum analog of the Nagelsbach-Kostka and Jacobi-Trudi formulae for the quantum double Schubert polynomials in the case of Grassmannian permutations. We prove, also, an analog of the Billey-Jockusch-Stanley formula for quantum...
Quantum entanglement and quantum operation
Institute of Scientific and Technical Information of China (English)
2008-01-01
It is a simple introduction to quantum entanglement and quantum operations.The authors focus on some applications of quantum entanglement and relations between two-qubit entangled states and unitary operations.It includes remote state preparation by using any pure entangled states,nonlocal operation implementation using entangled states,entanglement capacity of two-qubit gates and two-qubit gates construction.
Quantum learning without quantum memory
Sentís, G.; Calsamiglia, J.; Muñoz-Tapia, R; Bagan, E.
2012-01-01
A quantum learning machine for binary classification of qubit states that does not require quantum memory is introduced and shown to perform with the minimum error rate allowed by quantum mechanics for any size of the training set. This result is shown to be robust under (an arbitrary amount of) noise and under (statistical) variations in the composition of the training set, provided it is large enough. This machine can be used an arbitrary number of times without retraining. Its required cla...
Quantum group and quantum symmetry
International Nuclear Information System (INIS)
This is a self-contained review on the theory of quantum group and its applications to modern physics. A brief introduction is given to the Yang-Baxter equation in integrable quantum field theory and lattice statistical physics. The quantum group is primarily introduced as a systematic method for solving the Yang-Baxter equation. Quantum group theory is presented within the framework of quantum double through quantizing Lie bi-algebra. Both the highest weight and the cyclic representations are investigated for the quantum group and emphasis is laid on the new features of representations for q being a root of unity. Quantum symmetries are explored in selected topics of modern physics. For a Hamiltonian system the quantum symmetry is an enlarged symmetry that maintains invariance of equations of motion and allows a deformation of the Hamiltonian and symplectic form. The configuration space of the integrable lattice model is analyzed in terms of the representation theory of quantum group. By means of constructing the Young operators of quantum group, the Schroedinger equation of the model is transformed to be a set of coupled linear equations that can be solved by the standard method. Quantum symmetry of the minimal model and the WZNW model in conformal field theory is a hidden symmetry expressed in terms of screened vertex operators, and has a deep interplay with the Virasoro algebra. In quantum group approach a complete description for vibrating and rotating diatomic molecules is given. The exact selection rules and wave functions are obtained. The Taylor expansion of the analytic formulas of the approach reproduces the famous Dunham expansion. (author). 133 refs, 20 figs
Quantum Physics Without Quantum Philosophy
Dürr, Detlef; Zanghì, Nino
2013-01-01
It has often been claimed that without drastic conceptual innovations a genuine explanation of quantum interference effects and quantum randomness is impossible. This book concerns Bohmian mechanics, a simple particle theory that is a counterexample to such claims. The gentle introduction and other contributions collected here show how the phenomena of non-relativistic quantum mechanics, from Heisenberg's uncertainty principle to non-commuting observables, emerge from the Bohmian motion of particles, the natural particle motion associated with Schrödinger's equation. This book will be of value to all students and researchers in physics with an interest in the meaning of quantum theory as well as to philosophers of science.
Two-dimensional quantum ferromagnet with different spins: a Greens's function approach
International Nuclear Information System (INIS)
The magnetization of a two-dimensional ferromagnetic Heisenberg model, which represents a quantum Hall system at filling factor v=1, is calculated employing Green's function approach. The calculations are discussed in detail for spins S = 1/2, 1 and 3/2. The result for S = 1/2 is compared with recent quantum Monte Carlo simulations (Authors)
International Nuclear Information System (INIS)
The Monte Carlo code MONK is a general program written to provide a high degree of flexibility to the user. MONK is distinguished by its detailed representation of nuclear data in point form i.e., the cross-section is tabulated at specific energies instead of the more usual group representation. The nuclear data are unadjusted in the point form but recently the code has been modified to accept adjusted group data as used in fast and thermal reactor applications. The various geometrical handling capabilities and importance sampling techniques are described. In addition to the nuclear data aspects, the following features are also described; geometrical handling routines, tracking cycles, neutron source and output facilities. 12 references. (U.S.)
Monte Carlo lattice program KIM
International Nuclear Information System (INIS)
The Monte Carlo program KIM solves the steady-state linear neutron transport equation for a fixed-source problem or, by successive fixed-source runs, for the eigenvalue problem, in a two-dimensional thermal reactor lattice. Fluxes and reaction rates are the main quantities computed by the program, from which power distribution and few-group averaged cross sections are derived. The simulation ranges from 10 MeV to zero and includes anisotropic and inelastic scattering in the fast energy region, the epithermal Doppler broadening of the resonances of some nuclides, and the thermalization phenomenon by taking into account the thermal velocity distribution of some molecules. Besides the well known combinatorial geometry, the program allows complex configurations to be represented by a discrete set of points, an approach greatly improving calculation speed
Monte Carlo application tool-kit (MCATK)
International Nuclear Information System (INIS)
The Monte Carlo Application tool-kit (MCATK) is a C++ component-based software library designed to build specialized applications and to provide new functionality for existing general purpose Monte Carlo radiation transport codes such as MCNP. We will describe MCATK and its capabilities along with presenting some verification and validations results. (authors)
Quantum information. Teleportation - cryptography - quantum computer
International Nuclear Information System (INIS)
The following topics are dealt with: Reality in the test facility, quantum teleportation, the reality of quanta, interaction-free quantum measurement, rules for quantum computers, quantum computers with ions, spintronics with diamond, the limits of the quantum computers, a view in the future of quantum optics. (HSI)
Quantum Homogeneous Spaces as Quantum Quotient Spaces
Brzezinski, Tomasz
1995-01-01
We show that certain embeddable homogeneous spaces of a quantum group that do not correspond to a quantum subgroup still have the structure of quantum quotient spaces. We propose a construction of quantum fibre bundles on such spaces. The quantum plane and the general quantum two-spheres are discussed in detail.
Probing loop quantum gravity with evaporating black holes.
Barrau, A; Cailleteau, T; Cao, X; Diaz-Polo, J; Grain, J
2011-12-16
This Letter aims at showing that the observation of evaporating black holes should allow the usual Hawking behavior to be distinguished from loop quantum gravity (LQG) expectations. We present a full Monte Carlo simulation of the evaporation in LQG and statistical tests that discriminate between competing models. We conclude that contrarily to what was commonly thought, the discreteness of the area in LQG leads to characteristic features that qualify evaporating black holes as objects that could reveal quantum gravity footprints. PMID:22243065
Optimization by Quantum Annealing: Lessons from hard 3-SAT cases
Battaglia, Demian; Santoro, Giuseppe; Tosatti, Erio
2005-01-01
The Path Integral Monte Carlo simulated Quantum Annealing algorithm is applied to the optimization of a large hard instance of the Random 3-SAT Problem (N=10000). The dynamical behavior of the quantum and the classical annealing are compared, showing important qualitative differences in the way of exploring the complex energy landscape of the combinatorial optimization problem. At variance with the results obtained for the Ising spin glass and for the Traveling Salesman Problem, in the presen...
Feasibility of underwater free space quantum key distribution
Shi, Peng; Li, Wen-Dong; Gu, Yong-Jian
2014-01-01
We investigate the optical absorption and scattering properties of underwater media pertinent to our underwater quantum key distribution (QKD) channel model. With the vector radiative transfer theory and Monte Carlo method, we calculate the bit rate, the fidelity, and the quantum bit error rate of photons when transmitting underwater. It can be observed from our simulations that maximally secure single photon underwater BB84 QKD is feasible with a distance of about 125m in the clearest ocean water.
International Nuclear Information System (INIS)
Issues arising in the application of quantum mechanics to the universe as a whole are discussed. The inevitable need for a theory of initial conditions in making quantum mechanical predictions is emphasized and some proposals for theories of initial conditions are described. (author)
Manning, Phillip
2011-01-01
The study of quantum theory allowed twentieth-century scientists to examine the world in a new way, one that was filled with uncertainties and probabilities. Further study also led to the development of lasers, the atomic bomb, and the computer. This exciting new book clearly explains quantum theory and its everyday uses in our world.
Monte Carlo study of double exchange interaction in manganese oxide
International Nuclear Information System (INIS)
In this paper we study the magnetoresistance properties attributed by double exchange (DE) interaction in manganese oxide by Monte Carlo simulation. We construct a model based on mixed-valence Mn3+ and Mn4+ on the general system of Re2/3Ae1/3MnO3 in two dimensional system. The conduction mechanism is based on probability of eg electrons hopping from Mn3+ to Mn4+. The resistivity dependence on temperature and the external magnetic field are presented and the validity with related experimental results are discussed. We use the resistivity power law to fit our data on metallic region and basic activated behavior on insulator region. On metallic region, we found our result agree well with the quantum theory of DE interaction. From general arguments, we found our simulation agree qualitatively with experimental results
Monte Carlo study of double exchange interaction in manganese oxide
Energy Technology Data Exchange (ETDEWEB)
Naa, Christian Fredy, E-mail: chris@cphys.fi.itb.ac.id [Physics Department, Faculty of Mathematics and Natural Science, Institut Teknologi Bandung, Jalan Ganesha 10 Bandung (Indonesia); Unité de Dynamique et Structure des Matérioux Moléculaires, Université Littoral Côte d’Opale, Maison de la Reserche Blaise Pascal 50, rue Ferdinand Buisson, Calais, France email (France); Suprijadi,, E-mail: supri@fi.itb.ac.id; Viridi, Sparisoma, E-mail: dudung@fi.itb.ac.id; Djamal, Mitra, E-mail: mitra@fi.itb.ac.id [Physics Department, Faculty of Mathematics and Natural Science, Institut Teknologi Bandung, Jalan Ganesha 10 Bandung (Indonesia); Fasquelle, Didier, E-mail: didier.fasquelle@univ-littoral.fr [Unité de Dynamique et Structure des Matérioux Moléculaires, Université Littoral Côte d’Opale, Maison de la Reserche Blaise Pascal 50, rue Ferdinand Buisson, Calais, France email (France)
2015-09-30
In this paper we study the magnetoresistance properties attributed by double exchange (DE) interaction in manganese oxide by Monte Carlo simulation. We construct a model based on mixed-valence Mn{sup 3+} and Mn{sup 4+} on the general system of Re{sub 2/3}Ae{sub 1/3}MnO{sub 3} in two dimensional system. The conduction mechanism is based on probability of e{sub g} electrons hopping from Mn{sup 3+} to Mn{sup 4+}. The resistivity dependence on temperature and the external magnetic field are presented and the validity with related experimental results are discussed. We use the resistivity power law to fit our data on metallic region and basic activated behavior on insulator region. On metallic region, we found our result agree well with the quantum theory of DE interaction. From general arguments, we found our simulation agree qualitatively with experimental results.
Common misconceptions in Monte Carlo particle transport
Energy Technology Data Exchange (ETDEWEB)
Booth, Thomas E., E-mail: teb@lanl.gov [LANL, XCP-7, MS F663, Los Alamos, NM 87545 (United States)
2012-07-15
Monte Carlo particle transport is often introduced primarily as a method to solve linear integral equations such as the Boltzmann transport equation. This paper discusses some common misconceptions about Monte Carlo methods that are often associated with an equation-based focus. Many of the misconceptions apply directly to standard Monte Carlo codes such as MCNP and some are worth noting so that one does not unnecessarily restrict future methods. - Highlights: Black-Right-Pointing-Pointer Adjoint variety and use from a Monte Carlo perspective. Black-Right-Pointing-Pointer Misconceptions and preconceived notions about statistical weight. Black-Right-Pointing-Pointer Reasons that an adjoint based weight window sometimes works well or does not. Black-Right-Pointing-Pointer Pulse height/probability of initiation tallies and 'the' transport equation. Black-Right-Pointing-Pointer Highlights unnecessary preconceived notions about Monte Carlo transport.
Rae, Alastair I M
2016-01-01
A Thorough Update of One of the Most Highly Regarded Textbooks on Quantum Mechanics Continuing to offer an exceptionally clear, up-to-date treatment of the subject, Quantum Mechanics, Sixth Edition explains the concepts of quantum mechanics for undergraduate students in physics and related disciplines and provides the foundation necessary for other specialized courses. This sixth edition builds on its highly praised predecessors to make the text even more accessible to a wider audience. It is now divided into five parts that separately cover broad topics suitable for any general course on quantum mechanics. New to the Sixth Edition * Three chapters that review prerequisite physics and mathematics, laying out the notation, formalism, and physical basis necessary for the rest of the book * Short descriptions of numerous applications relevant to the physics discussed, giving students a brief look at what quantum mechanics has made possible industrially and scientifically * Additional end-of-chapter problems with...
International Nuclear Information System (INIS)
Quantum minigolf is a virtual-reality computer game visualizing quantum mechanics. The rules are the same as for the classical game minigolf, the goal being to kick a ball such that it crosses an obstacle course and runs into a hole. The ball, however, follows the laws of quantum mechanics: It can be at several places at once or tunnel through obstacles. To know whether the ball has reached the goal, the player has to perform a position measurement, which converts the ball into a classical object and fixes its position. But quantum mechanics is indeterministic: There is always a chance to lose, even for Tiger Woods. Technically, the obstacle course and the ball are projected onto the floor by a video projector. The position of the club is tracked by an infrared marker, similar as in Nintendo's Wii console. The whole setup is portable and the software has been published under the GPL license on www.quantum-minigolf.org.
Richter, Johannes; Farnell, Damian; Bishop, Raymod
2004-01-01
The investigation of magnetic systems where quantum effects play a dominant role has become a very active branch of solid-state-physics research in its own right. The first three chapters of the "Quantum Magnetism" survey conceptual problems and provide insights into the classes of systems considered, namely one-dimensional, two-dimensional and molecular magnets. The following chapters introduce the methods used in the field of quantum magnetism, including spin wave analysis, exact diagonalization, quantum field theory, coupled cluster methods and the Bethe ansatz. The book closes with a chapter on quantum phase transitions and a contribution that puts the wealth of phenomena into the context of experimental solid-state physics. Closing a gap in the literature, this volume is intended both as an introductory text at postgraduate level and as a modern, comprehensive reference for researchers in the field.
Hadjiivanov, Ludmil
2015-01-01
Expository paper providing a historical survey of the gradual transformation of the "philosophical discussions" between Bohr, Einstein and Schr\\"odinger on foundational issues in quantum mechanics into a quantitative prediction of a new quantum effect, its experimental verification and its proposed (and loudly advertised) applications. The basic idea of the 1935 paper of Einstein-Podolsky-Rosen (EPR) was reformulated by David Bohm for a finite dimensional spin system. This allowed John Bell to derive his inequalities that separate the prediction of quantum entanglement from its possible classical interpretation. We reproduce here their later (1971) version, reviewing on the way the generalization (and mathematical derivation) of Heisenberg's uncertainty relations (due to Weyl and Schr\\"odinger) needed for the passage from EPR to Bell. We also provide an improved derivation of the quantum theoretic violation of Bell's inequalities. Soon after the experimental confirmation of the quantum entanglement (culminati...
Cariolaro, Gianfranco
2015-01-01
This book demonstrates that a quantum communication system using the coherent light of a laser can achieve performance orders of magnitude superior to classical optical communications Quantum Communications provides the Masters and PhD signals or communications student with a complete basics-to-applications course in using the principles of quantum mechanics to provide cutting-edge telecommunications. Assuming only knowledge of elementary probability, complex analysis and optics, the book guides its reader through the fundamentals of vector and Hilbert spaces and the necessary quantum-mechanical ideas, simply formulated in four postulates. A turn to practical matters begins with and is then developed by: · development of the concept of quantum decision, emphasizing the optimization of measurements to extract useful information from a quantum system; · general formulation of a transmitter–receiver system · particular treatment of the most popular quantum co...
H2 Adsorption in a Porous Crystal: Accurate First-Principles Quantum Simulation.
D'Arcy, Jordan H; Jordan, Meredith J T; Frankcombe, Terry J; Collins, Michael A
2015-12-17
A general method is presented for constructing, from ab initio quantum chemistry calculations, the potential energy surface (PES) for H2 absorbed in a porous crystalline material. The method is illustrated for the metal-organic framework material MOF-5. Rigid body quantum diffusion Monte Carlo simulations are used in the construction of the PES and to evaluate the quantum ground state of H2 in MOF-5, the zero-point energy, and the enthalpy of adsorption at 0 K. PMID:26322374
Computing the distance between quantum channels: usefulness of the Fano representation
Benenti, Giuliano; Strini, Giuliano
2010-01-01
Abstract The diamond norm measures the distance between two quantum channels. From an operational vewpoint, this norm measures how well we can distinguish between two channels by applying them to input states of arbitrarily large dimensions. In this paper, we show that the diamond norm can be conveniently and in a physically transparent way computed by means of a Monte-Carlo algorithm based on the Fano representation of quantum states and quantum operations. The effectiveness of this algor...
Simulated Quantum Annealing Can Be Exponentially Faster than Classical Simulated Annealing
Crosson, Elizabeth; Harrow, Aram W.
2016-01-01
Simulated Quantum Annealing (SQA) is a Markov Chain Monte-Carlo algorithm that samples the equilibrium thermal state of a Quantum Annealing (QA) Hamiltonian. In addition to simulating quantum systems, SQA has also been proposed as another physics-inspired classical algorithm for combinatorial optimization, alongside classical simulated annealing. However, in many cases it remains an open challenge to determine the performance of both QA and SQA. One piece of evidence for the strength of Q...
International Nuclear Information System (INIS)
This textbook for students of physics is oriented in the selection of matter by the contents of a two-semester course about quantum theory. Thereby the foundations of quantum theory, among them the quantum-mechanical measurement process, the mathematical formalism, and Bell's inequalities, are extensively treated. Also modern concepts like feynman's path integral are regarded. This work is equally suited for a self-study, as course-accompanying lecture, and for preparations of examina. Application examples, supplementary explanations, and numerous illustration take car for a good understanding of the theoretical contents
Gudder, Stanley P
2014-01-01
Quantum probability is a subtle blend of quantum mechanics and classical probability theory. Its important ideas can be traced to the pioneering work of Richard Feynman in his path integral formalism.Only recently have the concept and ideas of quantum probability been presented in a rigorous axiomatic framework, and this book provides a coherent and comprehensive exposition of this approach. It gives a unified treatment of operational statistics, generalized measure theory and the path integral formalism that can only be found in scattered research articles.The first two chapters survey the ne
Lowe, John P
1993-01-01
Praised for its appealing writing style and clear pedagogy, Lowe's Quantum Chemistry is now available in its Second Edition as a text for senior undergraduate- and graduate-level chemistry students. The book assumes little mathematical or physical sophistication and emphasizes an understanding of the techniques and results of quantum chemistry, thus enabling students to comprehend much of the current chemical literature in which quantum chemical methods or concepts are used as tools. The book begins with a six-chapter introduction of standard one-dimensional systems, the hydrogen atom,
Powell, John L
2015-01-01
Suitable for advanced undergraduates, this thorough text focuses on the role of symmetry operations and the essentially algebraic structure of quantum-mechanical theory. Based on courses in quantum mechanics taught by the authors, the treatment provides numerous problems that require applications of theory and serve to supplement the textual material.Starting with a historical introduction to the origins of quantum theory, the book advances to discussions of the foundations of wave mechanics, wave packets and the uncertainty principle, and an examination of the Schrödinger equation that includ
Collins, D; Gisin, Nicolas; Massar, S; Popescu, S
2004-01-01
The slogan "information is physical" has been so successful that it led to some excess. Classical and quantum information can be thought of independently of any physical implementation. Pure information tasks can be realized using such abstract c- and qu-bits, but physical tasks require appropriate physical realizations of c- or qu-bits. As illustration we consider the problem of communicating chirality. We discuss in detail the physical resources this necessitates, and introduce the natural concept of "quantum gloves", i.e. rotationally invariant quantum states that encode as much as possible the concept of chirality and nothing more.
International Nuclear Information System (INIS)
This book, based on a thirty lecture course given to students at the beginning of their second year, covers the quantum mechanics required by physics undergraduates. Early chapters deal with wave mechanics, including a discussion of the energy states of the hydrogen atom. These are followed by a more formal development of the theory, leading to a discussion of some advanced applications and an introduction to the conceptual problems associated with quantum measurement theory. Emphasis is placed on the fundamentals of quantum mechanics. Problems are included at the end of each chapter. (U.K.)
Fateev, Evgeny G
2013-01-01
The principles of quantum motors based on Casimir platforms (thin-film nanostructures are at issue) are discussed in plain language. The generation of quantum propulsion is caused by the noncompensated integral action of virtual photon momenta upon a configuration unit cell in the platform. The cells in a Casimir platform should be situated in a certain order with optimal geometric parameters. The evaluation of the quantum propulsion shows that, for example, ten square meters of ideal Casimir platforms (it is a complex single-layer structure) could make Cheops pyramid move!
Tsekov, R.
2012-01-01
The Brownian motion of a light quantum particle in a heavy classical gas is theoretically described and a new expression for the friction coefficient is obtained for arbitrary temperature. At zero temperature it equals to the de Broglie momentum of the mean free path divided by the mean free path. Alternatively, the corresponding mobility of the quantum particle in the classical gas is equal to the square of the mean free path divided by the Planck constant. The Brownian motion of a quantum p...
Quantum Computers and Quantum Computer Languages: Quantum Assembly Language and Quantum C
Blaha, Stephen
2002-01-01
We show a representation of Quantum Computers defines Quantum Turing Machines with associated Quantum Grammars. We then create examples of Quantum Grammars. Lastly we develop an algebraic approach to high level Quantum Languages using Quantum Assembly language and Quantum C language as examples.
Quantum Computers and Quantum Computer Languages: Quantum Assembly Language and Quantum C Language
Blaha, Stephen
2002-01-01
We show a representation of Quantum Computers defines Quantum Turing Machines with associated Quantum Grammars. We then create examples of Quantum Grammars. Lastly we develop an algebraic approach to high level Quantum Languages using Quantum Assembly language and Quantum C language as examples.
Institute of Scientific and Technical Information of China (English)
ZHOU Nan-run; GONG Li-hua; LIU Ye
2006-01-01
In this letter a cascade quantum teleportation scheme is proposed. The proposed scheme needs less local quantum operations than those of quantum multi-teleportation. A quantum teleportation scheme based on entanglement swapping is presented and compared with the cascade quantum teleportation scheme. Those two schemes can effectively teleport quantum information and extend the distance of quantum communication.
Quantum group gauge theory on quantum spaces
Brzezinski, Tomasz; Majid, Shahn
1992-01-01
We construct quantum group-valued canonical connections on quantum homogeneous spaces, including a q-deformed Dirac monopole on the quantum sphere of Podles quantum differential coming from the 3-D calculus of Woronowicz on $SU_q(2)$ . The construction is presented within the setting of a general theory of quantum principal bundles with quantum group (Hopf algebra) fiber, associated quantum vector bundles and connection one-forms. Both the base space (spacetime) and the total space are non-co...
Exclusive quantum channels in quantum networks
Chen, Xi; Wang, He-Ming; Mu, Liang-Zhu; Fan, Heng
2014-01-01
Quantum state can be teleported to a remote site by only local measurement and classical communication if the prior Einstein-Podolsky-Rosen quantum channel is available between the sender and the receiver. Those quantum channels shared by multiple nodes can constitute a quantum network. Yet, studies on the efficiency of quantum communication between nodes of quantum networks remain limited, which differs from classical case in that the quantum channel will be consumed if teleportation is perf...
Use of Monte Carlo Methods in brachytherapy
International Nuclear Information System (INIS)
The Monte Carlo method has become a fundamental tool for brachytherapy dosimetry mainly because no difficulties associated with experimental dosimetry. In brachytherapy the main handicap of experimental dosimetry is the high dose gradient near the present sources making small uncertainties in the positioning of the detectors lead to large uncertainties in the dose. This presentation will review mainly the procedure for calculating dose distributions around a fountain using the Monte Carlo method showing the difficulties inherent in these calculations. In addition we will briefly review other applications of the method of Monte Carlo in brachytherapy dosimetry, as its use in advanced calculation algorithms, calculating barriers or obtaining dose applicators around. (Author)