Ferromagnetism and d-wave superconductivity in the 2D Hubbard model
By using the functional renormalization group we compute detailed momentum dependencies of the scale-dependent interaction vertex of the 2D (t,t')-Hubbard model. Compared to previous studies we improve accuracy by separating dominant parts from a remainder term. The former explicitly describe, for example, the interaction of Cooper pairs or spin operators. Applying the method to the repulsive Hubbard model we find d-wave superconductivity or ferromagnetism for larger next-to-nearest neighbor hopping amplitude t' at Van Hove Filling. Both ordering tendencies strongly compete with each other.
On a superconducting instability in the 2D repulsive Hubbard model at low occupancy
A Cooper instability for a weakly interacting 2D repulsive Hubbard model on a square lattice is found at low fermion occupancy. The point is that the previously known results concerning superconductivity under the conditions presented claim the absence of both s- and p-pairings when only nearest neighbors are accounted for. Taking into account next-to-nearest hopping terms in the Hamiltonian one can change the situation so that the l=1 partial scattering amplitude becomes singular. (author). 6 refs
Systematic study of d-wave superconductivity in the 2D repulsive Hubbard model
Maier, T. A.; Jarrell, M.; Schulthess, T.C.; Kent, P. R. C.; White, J. B.
2005-01-01
The cluster size dependence of superconductivity in the conventional two-dimensional Hubbard model, commonly believed to describe high-temperature superconductors, is systematically studied using the Dynamical Cluster Approximation and Quantum Monte Carlo simulations as cluster solver. Due to the non-locality of the d-wave superconducting order parameter, the results on small clusters show large size and geometry effects. In large enough clusters, the results are independent of the cluster si...
Absence of the d-Density Wave State in 2D Hubbard Model
Macridin, Alexandru; Jarrell, Mark; Maier, Thomas
2004-01-01
Using the Dynamical Cluster Approximation (DCA) we calculate the alternating circulating-current susceptibility and investigate the transition to the d-density wave (DDW) order in the two-dimensional Hubbard model. The 2 x 2 cluster used in the DCA calculation is the smallest that can capture d-wave order; therefore, due to the mean-field character of our calculation, we expect to overestimate d-wave transition temperatures. Despite this, we found no transition to the DDW state. In the pseudo...
A dimensional scaling computation of the electron concentration-dependent ground-state energy for the repulsive Hubbard model is presented, a generalization of Capelle’s analysis of the 2D and 3D Hubbard Hamiltonians with half-filled bands. The computed ground-state energies are compared with the results of mean-field and density matrix functional theories and of quantum Monte Carlo calculations. The comparison indicates that dimensional scaling yields moderately accurate ground-state energies close to and at half filling over the wide range of interaction strengths in the study. By contrast, the accuracy becomes poor at low filling for strong interactions. (author)
Results are presented for the competition between d-wave superconductivity (dSC) and antiferromagnetism (AF) in the ground state of the two-dimensional (2D) Hubbard model, relevant for the high-Tc superconductors (HTSC). Using the variational cluster approach (VCA) we are able to resolve the low energy features at zero temperature and to calculate the spectral function for any wave vector in the Brillouin zone. The cluster calculations reproduce the overall ground-state phase diagram of the HTSC both for hole- and electron-doping. Consistent with experiments, the AF state is found to be significantly more robust for electron doping than for hole doping, resulting from the frustration induced by the next-nearest neighbor hopping in the Hubbard model. Moreover, the system shows a tendency to phase separation into a mixed AF-dSC phase at low and a pure dSC phase at higher doping, where the phase-separation energy is an order of magnitude larger for hole-doping
Maximum Probability Domains for Hubbard Models
Acke, Guillaume; Claeys, Pieter W; Van Raemdonck, Mario; Poelmans, Ward; Van Neck, Dimitri; Bultinck, Patrick
2015-01-01
The theory of Maximum Probability Domains (MPDs) is formulated for the Hubbard model in terms of projection operators and generating functions for both exact eigenstates as well as Slater determinants. A fast MPD analysis procedure is proposed, which is subsequently used to analyse numerical results for the Hubbard model. It is shown that the essential physics behind the considered Hubbard models can be exposed using MPDs. Furthermore, the MPDs appear to be in line with what is expected from Valence Bond Theory-based knowledge.
An algebraic approach to the Hubbard model
de Leeuw, Marius
2015-01-01
We study the algebraic structure of an integrable Hubbard-Shastry type lattice model associated with the centrally extended su(2|2) superalgebra. This superalgebra underlies Beisert's AdS/CFT worldsheet R-matrix and Shastry's R-matrix. The considered model specializes to the one-dimensional Hubbard model in a certain limit. We demonstrate that Yangian symmetries of the R-matrix specialize to the Yangian symmetry of the Hubbard model found by Korepin and Uglov. Moreover, we show that the Hubbard model Hamiltonian has an algebraic interpretation as the so-called secret symmetry. We also discuss Yangian symmetries of the A and B models introduced by Frolov and Quinn.
Ventura, P; Li, L; Sofia, S; Basu, S; Demarque, P
2009-01-01
Understanding the reasons of the cyclic variation of the total solar irradiance is one of the most challenging targets of modern astrophysics. These studies prove to be essential also for a more climatologic issue, associated to the global warming. Any attempt to determine the solar components of this phenomenon must include the effects of the magnetic field, whose strength and shape in the solar interior are far from being completely known. Modelling the presence and the effects of a magnetic field requires a 2D approach, since the assumption of radial symmetry is too limiting for this topic. We present the structure of a 2D evolution code that was purposely designed for this scope; rotation, magnetic field and turbulence can be taken into account. Some preliminary results are presented and commented.
Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model.
Chen, Cheng-Chien; Muechler, Lukas; Car, Roberto; Neupert, Titus; Maciejko, Joseph
2016-08-26
We study the two-dimensional (2D) Hubbard model using exact diagonalization for spin-1/2 fermions on the triangular and honeycomb lattices decorated with a single hexagon per site. In certain parameter ranges, the Hubbard model maps to a quantum compass model on those lattices. On the triangular lattice, the compass model exhibits collinear stripe antiferromagnetism, implying d-density wave charge order in the original Hubbard model. On the honeycomb lattice, the compass model has a unique, quantum disordered ground state that transforms nontrivially under lattice reflection. The ground state of the Hubbard model on the decorated honeycomb lattice is thus a 2D fermionic symmetry-protected topological phase. This state-protected by time-reversal and reflection symmetries-cannot be connected adiabatically to a free-fermion topological phase. PMID:27610869
Towards a Holographic Bose-Hubbard Model
Fujita, Mitsutoshi; Karch, Andreas; Meyer, Rene; Paquette, Natalie M
2014-01-01
We present a holographic construction of the large-N Bose-Hubbard model. The model is based on Maxwell fields coupled to charged scalar fields on the AdS2 hard wall. We realize the lobe-shaped phase structure of the Bose-Hubbard model and find that the model admits Mott insulator ground states in the limit of large Coulomb repulsion. In the Mott insulator phases, the bosons are localized on each site. At zero hopping we find that the transitions between Mott insulating phases with different fillings correspond to first order level-crossing phase transitions. At finite hopping we find a holographic phase transition between the Mott phase and a non-homogeneous phase. We then analyze the perturbations of fields around both the Mott insulator phase and inhomogeneous phase. We find an almost zero mode in the non-homogeneous phase.
Phase separation in the Hubbard model
Macridin, A.; Jarrell, M.; Maier, Th.
2005-01-01
Phase separation in the Hubbard model is investigated with the dynamical cluster approximation. We find that it is present in the paramagnetic solution for values of filling smaller than one and at finite temperature when a positive next-nearest neighbor hopping is considered. The phase separated region is characterized by a mixture of a strongly correlated metallic and Mott insulating phases. Our results indicate that phase separation is driven by the formation of doped regions with strong a...
Mott transition in the Hubbard model
In this article, the author discuss W. Kohn's criterion for a metal insulator transition, within the framework of a one-band Hubbard model. This and related ideas are applied to 1-dimensional Hubbard systems, and some interesting miscellaneous results discussed. The Jordan-Wigner transformation converting the two species of fermions to two species of hardcore bosons is performed in detail, and the extra phases arising from odd-even effects are explicitly derived. Bosons are shown to prefer zero flux (i.e., diamagnetism) and the corresponding happy fluxes: for the fermions identified. A curios result following from the interplay between orbital diamagnetism and spin polarization is highlighted. A spin-statistics like theorem, showing that the anticommutation relations between fermions of opposite spin are crucial to obtain the SU(2) invariance is pointed out
Activated sludge model No. 2d, ASM2d
Henze, M.
1999-01-01
The Activated Sludge Model No. 2d (ASM2d) presents a model for biological phosphorus removal with simultaneous nitrification-denitrification in activated sludge systems. ASM2d is based on ASM2 and is expanded to include the denitrifying activity of the phosphorus accumulating organisms (PAOs...
Superconducting properties of the attractive Hubbard model
A self-consistent set of equations for the one-electron self-energy in the ladder approximation is derived for the attractive Hubbard model in the superconducting state. The equations provide an extension of a T-matrix formalism recently used to study the effect of electron correlations on normal-state properties. An approximation to the set of equations is solved numerically in the intermediate coupling regime, and the one-particle spectral functions are found to have four peaks. This feature is traced back to a peak in the self-energy, which is related to the formation of real-space bound states. For comparison we extend the moment approach to the superconducting state and discuss the crossover from the weak (BCS) to the intermediate coupling regime from the perspective of single-particle spectral densities. (orig.)
Electron-phonon interaction in the Hubbard model
Superconductivity existence in the Hubbard model is studied, taking into account both electron-phonon and electron-electron interactions. Using Sarker's functional integral formalism a system of equations for the dynamical order parameters is derived. (author). 7 refs
Reexamination of the variational Bose-Hubbard model
Major, Jan; Łącki, Mateusz; Zakrzewski, Jakub
2014-04-01
For strongly interacting bosons in optical lattices, the standard description using the Bose-Hubbard model becomes questionable. The role of excited bands becomes important. In such a situation, we compare results of simulations using the multiband Bose-Hubbard model with a recent proposition based on a time-dependent variational approach. It is shown that the latter, in its original formulation, uses a too small variational space, often leading to spurious effects. Possible expansion of the variational approach is discussed.
Flow equations for the ionic Hubbard model
Hafez, Mohsen; Jafari, S. A.; Abolhassani, M. R.
2009-12-01
Taking the site-diagonal terms of the ionic Hubbard model (IHM) in one and two spatial dimensions, as H, we employ Continuous Unitary Transformations (CUT) to obtain a “classical” effective Hamiltonian in which hopping term has been renormalized to zero. For this Hamiltonian spin gap and charge gap are calculated at half-filling and subject to periodic boundary conditions. Our calculations indicate two transition points. In fixed Δ, as U increases from zero, there is a region in which both spin gap and charge gap are positive and identical; characteristic of band insulators. Upon further increasing U, first transition occurs at U=Uc_1, where spin and charge gaps both vanish and remain zero up to U=Uc_2. A gap-less state in charge and spin sectors characterizes a metal. For U>Uc_2 spin gap remains zero and charge gap becomes positive. This third region corresponds to a Mott insulator in which charge excitations are gaped, while spin excitations remain gap-less.
Hubbard operator density functional theory for Fermionic lattice models
Cheng, Zhengqian; Marianetti, Chris
We formulate an effective action as a functional of Hubbard operator densities whose stationary point delivers all local static information of the interacting lattice model. Using the variational principle, we get a self-consistent equation for Hubbard operator densities. The computational cost of our approach is set by diagonalizing the local Fock space. We apply our method to the one and two band Hubbard model (including crystal field and on-site exchange) in infinite dimensions where the exact solution is known. Excellent agreement is obtained for the one-band model. In the two-band model, good agreement is obtained in the metallic region of the phase diagram in addition to the metal-insulator transition. While our approach does not address frequency dependent observables, it has a negligible computational cost as compared to dynamical mean field theory and could be highly applicable in the context total energies of strongly correlated materials and molecules.
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.
A bespoke single-band Hubbard model material
Griffin, S. M.; Staar, P.; Schulthess, T. C.; Troyer, M.; Spaldin, N. A.
2016-02-01
The Hubbard model, which augments independent-electron band theory with a single parameter to describe electron-electron correlations, is widely regarded to be the "standard model" of condensed-matter physics. The model has been remarkably successful at addressing a range of correlation phenomena in solids, but it neglects many behaviors that occur in real materials, such as phonons, long-range interactions, and, in its simplest form, multiorbital effects. Here, we use ab initio electronic structure methods to design a material whose Hamiltonian matches as closely as possible that of the single-band Hubbard model. Our motivation is to compare the measured properties of our new material to those predicted by reliable theoretical solutions of the Hubbard model to determine the relevance of the model in the description of real materials. After identifying an appropriate crystal class and several appropriate chemistries, we use density-functional theory and dynamical mean-field theory to screen for the desired electronic band structure and metal-insulator transition. We then explore the most promising candidates for structural stability and suitability for doping, and we propose specific materials for subsequent synthesis. Finally, we identify a regime—that should manifest in our bespoke material—in which the single-band Hubbard model on a triangular lattice exhibits exotic d -wave superconductivity.
Critical points of the anyon-Hubbard model
Arcila-Forero, J.; Franco, R.; Silva-Valencia, J.
2016-07-01
Anyons are particles with fractional statistics that exhibit a nontrivial change in the wave function under an exchange of particles. Anyons can be considered to be a general category of particles that interpolate between fermions and bosons. We determined the position of the critical points of the one-dimensional anyon-Hubbard model, which was mapped to a modified Bose-Hubbard model where the tunneling depends on the local density and the interchange angle. We studied the latter model by using the density-matrix renormalization-group method and observed that gapped (Mott insulator) and gapless (superfluid) phases characterized the phase diagram, regardless of the value of the statistical angle. The phase diagram for higher densities was calculated and showed that the Mott lobes increase (decrease) as a function of the statistical angle (global density). The position of the critical point separating the gapped and gapless phases was found using quantum information tools, namely the block von Neumann entropy. We also studied the evolution of the critical point with the global density and the statistical angle and showed that the anyon-Hubbard model with a statistical angle θ =π /4 is in the same universality class as the Bose-Hubbard model with two-body interactions.
Ground state phase diagram of extended attractive Hubbard model
The ground state phase diagram of the extended Hubbard model with intraatomic attraction has been derived in the Hartree-Fock approximation formulated in terms of the Bogoliubov variational approach. For a given value of electron density, the nature of the ordered ground state depends essentially on the sign and the strength of the nearest neighbor coupling. (author)
Stability of ferromagnetism in Hubbard models with nearly flat bands
Whether spin-independent Coulomb interaction in an electron system can be the origin of ferromagnetism has been an open problem for a long time. Recently, a open-quotes constructiveclose quotes approach to this problem has been developed, and the existence of ferromagnetism in the ground states of certain Hubbard models was established rigorously. A special feature of these Hubbard models is that their lowest bands (in the corresponding single-electron problems) are completely flat. Here we study models obtained by adding small but arbitrary translation-invariant perturbation to the hopping Hamiltonian of these flat-band models. The resulting models have nearly flat lowest bands. We prove that the ferromagnetic state is stable against a single-spin flip provided that Coulomb interaction U is sufficiently large. (It is easily found that the same state is unstable against a single-spin flip of U is small enough.) We also prove upper and lower bounds for the dispersion relation of the lowest energy eigenstate with a single flipped spin, which bounds establish that the model has open-quotes healthyclose quotes spin-wave excitation. It is notable that the (local) stability of ferromagnetism is proved in nonsingular Hubbard models, in which we must overcome competition between the kinetic energy and the Coulomb interaction. We also note that this is one of the very few rigorous and robust results which deal with truly non-perturbative phenomena in many-electron systems. The local stability strongly suggests that the Hubbard models with nearly flat bands have ferromagnetic ground states. We believe that the present models can be studied as paradigm models for (insulating) ferromagnetism in itinerant electron systems
Route to supersolidity for the extended Bose-Hubbard model
We use the Gutzwiller ansatz and analyze the phase diagram of the extended Bose-Hubbard Hamiltonian with on-site (U) and nearest-neighbor (V) repulsions. For d-dimensional hypercubic lattices, when 2dVU, in this Rapid Communication, we show that the ground state has only CDW insulators, and more importantly, the SS phase occupies a much larger region in the phase diagram, existing up to very large hopping values which could be orders of magnitude higher than that of the well-known case. In particular, the SS-superfluid phase boundary increases linearly as a function of hopping when 2dV > or approx. 1.5U, for which the prospects of observing the SS phase with dipolar Bose gases loaded into optical lattices is much higher.
The 2-site Hubbard and t-J models
Avella, Adolfo; Mancini, Ferdinando; Saikawa, Taiichiro
2001-01-01
The fermionic and bosonic sectors of the 2-site Hubbard model have been exactly solved by means of the equation of motion and Green's function formalism. The exact solution of the t-J model has been also reported to investigate the low-energy dynamics. We have successfully searched for the exact eigenoperators, and the corresponding eigenenergies, having in mind the possibility to use them as an operatorial basis on the lattice. Many local, single-particle, thermodynamical and response proper...
The 2-site Hubbard and {t}-{J} models
Avella, A.; Mancini, F.; Saikawa, T.
2003-12-01
The fermionic and bosonic sectors of the 2-site Hubbard model have been exactly solved by means of the equation of motion and Green’s function formalism. The exact solution of the t- J model has been also reported to investigate the low-energy dynamics. We have successfully searched for the exact eigenoperators, and the corresponding eigenenergies, having in mind the possibility to use them as an operatorial basis on the lattice. Many local, single-particle, thermodynamical and response properties have been studied as functions of the external parameters and compared between the two models and with some numerical and exact results. It has been shown that the 2-site Hubbard model already contains the most relevant energy scales of the Hubbard model: the local Coulomb interaction U and the spin-exchange one J = frac{4t^2}U. As a consequence of this, for some relevant properties (kinetic energy, double occupancy, energy, specific heat and entropy) and as regards the metal-insulator transition issue, it has resulted possible to almost exactly mime the behavior of larger systems, sometimes using a higher temperature to get a comparable level spacing. The 2-site models have been also used as toy models to test the efficiency of the Green’s function formalism for composite operators. The capability to reproduce the exact solutions, obtained by the exact diagonalization technique, gives a firm ground to the approximate treatments based on this formalism.
Equation of State of the Two-Dimensional Hubbard Model
Cocchi, Eugenio; Miller, Luke A.; Drewes, Jan H.; Koschorreck, Marco; Pertot, Daniel; Brennecke, Ferdinand; Köhl, Michael
2016-04-01
The subtle interplay between kinetic energy, interactions, and dimensionality challenges our comprehension of strongly correlated physics observed, for example, in the solid state. In this quest, the Hubbard model has emerged as a conceptually simple, yet rich model describing such physics. Here we present an experimental determination of the equation of state of the repulsive two-dimensional Hubbard model over a broad range of interactions 0 ≲U /t ≲20 and temperatures, down to kBT /t =0.63 (2 ) using high-resolution imaging of ultracold fermionic atoms in optical lattices. We show density profiles, compressibilities, and double occupancies over the whole doping range, and, hence, our results constitute benchmarks for state-of-the-art theoretical approaches.
Extended Bose-Hubbard models with ultracold magnetic atoms
Baier, S.; Mark, M. J.; Petter, D.; Aikawa, K.; Chomaz, L.; Cai, Z.; Baranov, M.; Zoller, P.; Ferlaino, F.
2016-04-01
The Hubbard model underlies our understanding of strongly correlated materials. Whereas its standard form only comprises interactions between particles at the same lattice site, extending it to encompass long-range interactions is predicted to profoundly alter the quantum behavior of the system. We realize the extended Bose-Hubbard model for an ultracold gas of strongly magnetic erbium atoms in a three-dimensional optical lattice. Controlling the orientation of the atomic dipoles, we reveal the anisotropic character of the onsite interaction and hopping dynamics and their influence on the superfluid-to-Mott insulator quantum phase transition. Moreover, we observe nearest-neighbor interactions, a genuine consequence of the long-range nature of dipolar interactions. Our results lay the groundwork for future studies of exotic many-body quantum phases.
Bose-Hubbard model on a checkerboard superlattice
Iskin, Menderes
2011-05-01
We study the ground-state phases of the Bose-Hubbard model on a checkerboard superlattice in two dimensions, including the superfluid phase and the Mott and charge-density-wave insulators. First, we discuss the single-particle Hofstadter problem, and show that the presence of a checkerboard superlattice gives rise to a magnetic flux-independent energy gap in the excitation spectrum. Then, we consider the many-particle problem, and derive an analytical mean-field expression for the superfluid-Mott and superfluid-charge-density-wave insulator phase transition boundaries. Finally, since the phase diagram of the Bose-Hubbard model on a checkerboard superlattice is in many ways similar to that of the extended Bose-Hubbard model, we comment on the effects of magnetic field on the latter model, and derive an analytical mean-field expression for the superfluid-insulator phase transition boundaries as well. This work is supported by Marie Curie International Reintegration Grant (FP7-PEOPLE-IRG-2010-268239).
The one-dimensional extended Bose-Hubbard model
Ramesh V Pai; Rahul Pandit
2003-10-01
We use the finite-size, density-matrix-renormalization-group (DMRG) method to obtain the zero-temperature phase diagram of the one-dimensional, extended Bose-Hubbard model, for mean boson density ρ = 1, in the - plane ( and are respectively, onsite and nearest-neighbour repulsive interactions between bosons). The phase diagram includes superfluid (SF), bosonic-Mott-insulator (MI), and mass-density-wave (MDW) phases. We determine the natures of the quantum phase transitions between these phases.
Local origin of the pseudogap in the attractive Hubbard model
PETERS, Robert; Bauer, Johannes
2015-01-01
We provide a new perspective on the pseudogap physics for attractive fermions as described by the three-dimensional Hubbard model. The pseudogap in the single-particle spectral function, which occurs for temperatures above the critical temperature $T_c$ of the superfluid transition, is often interpreted in terms of preformed, uncondensed pairs. Here we show that the occurrence of pseudogap physics can be consistently understood in terms of local excitations which lead to a splitting of the qu...
Iterated perturbation theory for the attractive Holstein and Hubbard models
Freericks, J. K.; Jarrell, Mark (Eds. )
1994-01-01
A strictly truncated (weak-coupling) perturbation theory is applied to the attractive Holstein and Hubbard models in infinite dimensions. These results are qualified by comparison with essentially exact Monte Carlo results. The second order iterated perturbation theory is shown to be quite accurate in calculating transition temperatures for retarded interactions, but is not as accurate for the self energy or the irreducible vertex functions themselves. Iterated perturbation theory is carried ...
Bond excitations in the pseudogap phase of the Hubbard Model
Macridin, Alexandru; Jarrell, Mark (Eds. )
2008-01-01
Using the dynamical cluster approximation, we calculate the correlation functions associated with the nearest neighbor bond operator which measure the z component of the spin exchange in the two-dimensional Hubbard model with $U$ equal to the bandwidth. We find that in the pseudogap region, the local bond susceptibility diverges at T=0. This shows the existence of degenerate bond spin excitation and implies quantum criticality and bond order formation when long range correlations are consider...
Entanglement entropies of the quarter filled Hubbard model
We study Rényi and von Neumann entanglement entropies in the ground state of the one dimensional quarter-filled Hubbard model with periodic boundary conditions. We show that they exhibit an unexpected dependence on system size: for L = 4mod 8 the results are in agreement with expectations based on conformal field theory, while for L = 0mod 8 additional contributions arise. We show that these can be understood in terms of a ‘shell-filling’ effect and we develop a conformal field theory approach to calculate the additional contributions to the entropies. These analytic results are found to be in excellent agreement with density matrix renormalization group computations for weak Hubbard interactions. We argue that for larger interactions the presence of a marginal irrelevant operator in the spin sector strongly affects the entropies at the finite sizes accessible numerically and we present an effective way to take them into account. (paper)
Entanglement entropies of the quarter filled Hubbard model
Calabrese, Pasquale; Essler, Fabian H. L.; Läuchli, Andreas M.
2014-09-01
We study Rényi and von Neumann entanglement entropies in the ground state of the one dimensional quarter-filled Hubbard model with periodic boundary conditions. We show that they exhibit an unexpected dependence on system size: for L = 4mod 8 the results are in agreement with expectations based on conformal field theory, while for L = 0mod 8 additional contributions arise. We show that these can be understood in terms of a ‘shell-filling’ effect and we develop a conformal field theory approach to calculate the additional contributions to the entropies. These analytic results are found to be in excellent agreement with density matrix renormalization group computations for weak Hubbard interactions. We argue that for larger interactions the presence of a marginal irrelevant operator in the spin sector strongly affects the entropies at the finite sizes accessible numerically and we present an effective way to take them into account.
Functional renormalization for antiferromagnetism and superconductivity in the Hubbard model
Despite its apparent simplicity, the two-dimensional Hubbard model for locally interacting fermions on a square lattice is widely considered as a promising approach for the understanding of Cooper pair formation in the quasi two-dimensional high-Tc cuprate materials. In the present work this model is investigated by means of the functional renormalization group, based on an exact flow equation for the effective average action. In addition to the fermionic degrees of freedom of the Hubbard Hamiltonian, bosonic fields are introduced which correspond to the different possible collective orders of the system, for example magnetism and superconductivity. The interactions between bosons and fermions are determined by means of the method of ''rebosonization'' (or ''flowing bosonization''), which can be described as a continuous, scale-dependent Hubbard-Stratonovich transformation. This method allows an efficient parameterization of the momentum-dependent effective two-particle interaction between fermions (four-point vertex), and it makes it possible to follow the flow of the running couplings into the regimes exhibiting spontaneous symmetry breaking, where bosonic fluctuations determine the types of order which are present on large length scales. Numerical results for the phase diagram are presented, which include the mutual influence of different, competing types of order. (orig.)
Functional renormalization for antiferromagnetism and superconductivity in the Hubbard model
Friederich, Simon
2010-12-08
Despite its apparent simplicity, the two-dimensional Hubbard model for locally interacting fermions on a square lattice is widely considered as a promising approach for the understanding of Cooper pair formation in the quasi two-dimensional high-T{sub c} cuprate materials. In the present work this model is investigated by means of the functional renormalization group, based on an exact flow equation for the effective average action. In addition to the fermionic degrees of freedom of the Hubbard Hamiltonian, bosonic fields are introduced which correspond to the different possible collective orders of the system, for example magnetism and superconductivity. The interactions between bosons and fermions are determined by means of the method of ''rebosonization'' (or ''flowing bosonization''), which can be described as a continuous, scale-dependent Hubbard-Stratonovich transformation. This method allows an efficient parameterization of the momentum-dependent effective two-particle interaction between fermions (four-point vertex), and it makes it possible to follow the flow of the running couplings into the regimes exhibiting spontaneous symmetry breaking, where bosonic fluctuations determine the types of order which are present on large length scales. Numerical results for the phase diagram are presented, which include the mutual influence of different, competing types of order. (orig.)
Path Integral Methods for Single Band Hubbard Model
N. Heydari; Azakov, S.
1997-01-01
We review various ways to express the partition function of the single-band Hubard model as a path integral. The emphasis is made on the derivation of the action in the integrand of the path integral and the results obtained from this approach are discussed only briefly. Since the single-band Hubbard model is a pure fermionic model on the lattice and its Hamiltonian is a polynomial in creation and annihilation fermionic operators, with the help of the fermionic coherent states of holomorp...
Spectral analysis of two-dimensional Bose-Hubbard models
Fischer, David; Hoffmann, Darius; Wimberger, Sandro
2016-04-01
One-dimensional Bose-Hubbard models are well known to obey a transition from regular to quantum-chaotic spectral statistics. We are extending this concept to relatively simple two-dimensional many-body models. Also in two dimensions a transition from regular to chaotic spectral statistics is found and discussed. In particular, we analyze the dependence of the spectral properties on the bond number of the two-dimensional lattices and the applied boundary conditions. For maximal connectivity, the systems behave most regularly in agreement with the applicability of mean-field approaches in the limit of many nearest-neighbor couplings at each site.
These are introductory lectures for a general audience that give an overview of the subject of matrix models and their application to random surfaces, 2d gravity, and string theory. They are intentionally 1.5 years out of date
Superconductivity in the two-dimensional generalized Hubbard model
Lima, L. S.
2016-08-01
We have used the Green's functions method at finite temperature and the Kubo's formalism, to calculate the electron conductivity σ(ω) in the generalized two-dimensional Hubbard model. We have obtained a behavior superconductor for the system to T > T0. The AC conductivity falls to zero in ω =ω0 , where ω0 depends on Δ, which is the gap of the system. The behavior gotten is according of with the behavior of the superconductors of high Tc where there is a changes abruptly from a Mott's insulator state to superconductor.
Bose–Hubbard model on two-dimensional line graphs
We construct a basis for the many-particle ground states of the positive hopping Bose–Hubbard model on line graphs of finite 2-connected planar bipartite graphs at sufficiently low filling factors. The particles in these states are localized on non-intersecting vertex-disjoint cycles of the line graph which correspond to non-intersecting edge-disjoint cycles of the original graph. The construction works up to a critical filling factor at which the cycles are close-packed. (paper)
Possible phase separation in square and honeycomb Hubbard model: A variational cluster study
Fang, Kun; Fernando, G.W. [Department of Physics, University of Connecticut, Storrs, CT 06269 (United States); Balatsky, A.V. [Institute for Materials Science, Los Alamos, NM 87545 (United States); NORDITA, Roslagstullsbacken 23, SE-106 91 Stockholm (Sweden); Kocharian, A.N., E-mail: armen.kocharian@calstatela.edu [Department of Physics, California State University, Los Angeles, CA 90032 (United States)
2015-10-02
The VCA ground state of the 2D Hubbard model is examined for possible phase separation under hole doping manifested by spatial inhomogeneities of coexisting different electron densities at equilibrium. Phase separation is accompanied by spectral weight loss and first Brillouin zone boundary deformation. Such an instability is observed in square structures and it is absent in honeycomb lattices. To our knowledge, no previous publications have revealed relationship between a Fermi surface instability and phase separation. Our VCA calculations provide strong support for this spontaneous instability, driven by electron correlations in specific lattice geometries, proposed in our earlier publications using exact quantum cluster calculations. - Highlights: • VCA study of possible spontaneous phase separation in 2D square and honeycomb Hubbard lattices. • Phase separation instabilities and density inhomogeneities driven by proximity to level crossing. • Contrasting differences in behaviors of spectral functions in square and honeycomb near first Brillouin zone. • VCA strongly confirms spontaneous phase separation obtained at level crossings in cluster calculations.
Possible phase separation in square and honeycomb Hubbard model: A variational cluster study
The VCA ground state of the 2D Hubbard model is examined for possible phase separation under hole doping manifested by spatial inhomogeneities of coexisting different electron densities at equilibrium. Phase separation is accompanied by spectral weight loss and first Brillouin zone boundary deformation. Such an instability is observed in square structures and it is absent in honeycomb lattices. To our knowledge, no previous publications have revealed relationship between a Fermi surface instability and phase separation. Our VCA calculations provide strong support for this spontaneous instability, driven by electron correlations in specific lattice geometries, proposed in our earlier publications using exact quantum cluster calculations. - Highlights: • VCA study of possible spontaneous phase separation in 2D square and honeycomb Hubbard lattices. • Phase separation instabilities and density inhomogeneities driven by proximity to level crossing. • Contrasting differences in behaviors of spectral functions in square and honeycomb near first Brillouin zone. • VCA strongly confirms spontaneous phase separation obtained at level crossings in cluster calculations
Magnetic properties of three-dimensional Hubbard-sigma model
It is broadly viewed that the magnetism may play an important role in the high-Tc superconductivity in the lamellar CuO2 materials. In this paper, based on a Hubbard-inspired CP1 or S2 nonlinear σ model, we give a quantitative study of some magnetic properties in and around the Neel ordered state of three-dimensional quantum antiferromagnets such as La2CuO4 with and without small hole doping. Our model is a (3+1) dimensional effective field theory describing the low energy spin dynamics of a three-dimensional Hubbard model with a very weak interlayer coupling. The effect of hole dynamics is taken into account in the leading approximation by substituting the CP1 coupling with an 'effective' one determined by the concentration and the one-loop correction of hole fermions. A stationary-phase equation for the one-loop effective potential of S2 model is analyzed numerically. The behavior of Neel temperature, magnetization (long range Neel order), spin correlation length, etc as functions of anisotropic parameter, temperature, hole concentrations, etc are investigated in detail. A phase diagram is also supported by the renormlization group analysis. The results show that our anisotropic field theory model with certain values of parameters could give a reasonably well description of the magnetic properties indicated by some experiments on pure and doped La2CuO4. (author)
Conservation laws in the one-dimensional Hubbard model
We examine the nature, number, and interrelation of conservation laws in the one-dimensional Hubbard model. In previous work by Shastry [Phys. Rev. Lett. 56, 1529 (1986); 56, 2334 (1986); 56, 2453 (1986); J. Stat. Phys. 50, 57 (1988)], who studied the model on a large but finite number of lattice sites (Na), only Na+1 conservation laws, corresponding to Na+1 operators that commute with themselves and the Hamiltonian, were explicitly identified, rather than the ∼2Na conservation laws expected from the solvability and integrability of the model. Using a pseudoparticle approach related to the thermodynamic Bethe ansatz, we discover an additional Na+1 independent conservation laws corresponding to nonlocal, mututally commuting operators, which we call transfer-matrix currents. Further, for the model defined in the whole Hilbert space, we find there are two other independent commuting operators (the squares of the η-spin and spin operators) so that the total number of local plus nonlocal commuting conservation laws for the one-dimensional Hubbard model is 2Na+4. Finally, we introduce an alternative set of 2Na+4 conservation laws which assume particularly simple forms in terms of the pseudoparticle and Yang-particle operators. This set of mutually commuting operators lends itself more readily to calculations of physically relevant correlation functions at finite energy or frequency than the previous set
In these lectures, I shall focus on the matrix formulation of 2-d gravity. In the first one, I shall discuss the main results of the continuum formulation of 2-d gravity, starting from the first renormalization group calculations which led to the concept of the conformal anomaly, going through the Polyakov bosonic string and the Liouville action, up to the recent results on the scaling properties of conformal field theories coupled to 2-d gravity. In the second lecture, I shall discuss the discrete formulation of 2-d gravity in term of random lattices, and the mapping onto random matrix models. The occurrence of critical points in the planar limit and the scaling limit at those critical points will be described, as well as the identification of these scaling limits with continuum 2-d gravity coupled to some matter field theory. In the third lecture, the double scaling limit in the one matrix model, and its connection with continuum non perturbative 2-d gravity, will be presented. The connection with the KdV hierarchy and the general form of the string equation will be discuted. In the fourth lecture, I shall discuss the non-perturbative effects present in the non perturbative solutions, in the case of pure gravity. The Schwinger-Dyson equations for pure gravity in the double scaling limit are described and their compatibility with the solutions of the string equation for pure gravity is shown to be somewhat problematic
Kuno, Yoshihito; Nakafuji, Takashi; Ichinose, Ikuo
2015-12-01
In this paper, we study Bose-Hubbard models on square and honeycomb lattices with complex hopping amplitudes, which are feasible by recent experiments of cold atomic gases in optical lattices. To clarify phase diagrams, we use extended quantum Monte Carlo simulations (eQMC). For the system on the square lattice, the complex hopping is realized by an artificial magnetic field. We found that vortex-solid states form for certain set of magnetic field, i.e., the magnetic field with the flux quanta per plaquette f =p /q , where p and q are co-prime natural numbers. For the system on the honeycomb lattice, we add the next-nearest-neighbor complex hopping. The model is a bosonic analog of the Haldane-Hubbard model. By means of eQMC, we study the model with both weak and strong onsite repulsions. Numerical study shows that the model has a rich phase diagram. We also found that in the system defined on the honeycomb lattice of the cylinder geometry, an interesting edge state appears.
Fermion Coherent State Studies of One-Dimensional Hubbard Model
LIN Ji; GAO Xian-Long; WANG Ke-Lin
2007-01-01
We present a comparative study of the ground state of the one-dimensional Hubbard model. We first use a new fermion coherent state method in the framework of Fermi liquid theory by introducing a hole operator and considering the interactions of two pairs electrons and holes. We construct the ground state of the Hubbard model as ｜〉 = [f + ∑′ψc+k1σ1 h+k2σ2 c+k3σ3 h+k4σ4 ∏exp(ρc+k1σ1 h+k2σ2)] [〉0, where ψ and ρ are the coupling constants. Our results are then compared to those of variational methods, density functional theory based on the exact solvable Bethe ansatz solutions, variational Monto-Carlo method (VMC) as well as to the exact result of the infinite system. We find satisfactory agreement between the fermion coherent state scheme and the VMC data, and provide a new picture to deal with the strongly correlated system.
Burcharth, Hans F.; Meinert, Palle; Andersen, Thomas Lykke
This report present the results of 2D physical model tests (length scale 1:50) carried out in a waveflume at Dept. of Civil Engineering, Aalborg University (AAU). The objective of the tests was: To identify cross section design which restrict the overtopping to acceptable levels and to record the...
Andersen, Thomas Lykke; Frigaard, Peter
This report present the results of 2D physical model tests carried out in the shallow wave flume at Dept. of Civil Engineering, Aalborg University (AAU), on behalf of Energy E2 A/S part of DONG Energy A/S, Denmark. The objective of the tests was: to investigate the combined influence of the pile...
Equation of state of the fermionic two-dimensional Hubbard model
LeBlanc, J. P. F.; Gull, Emanuel
2013-10-01
We present results for the equation of state of the two-dimensional Hubbard model on an isotropic square lattice as obtained from a controlled and numerically exact large-cluster dynamical mean field simulation. Our results are obtained for large but finite systems and are extrapolated to infinite system size using a known finite-size scaling relation, and are supplemented by reliable error bars accounting for all sources of errors. We establish the importance of examining the decay of spatial spin correlations to determine whether a sufficiently large cluster has been used and with this in mind we present the energy, entropy, double occupancy, and nearest-neighbor spin correlations extrapolated to the thermodynamic limit. We discuss the implications of these calculations on pseudogap physics of the 2D Hubbard model away from half filling, where we find a strong behavioral shift in energy below a temperature T* which becomes more pronounced for larger clusters. Finally, we provide reference calculations and tables for the equation of state for values of doping away from half filling which are of interest to cold-atom experiments.
Dynamical instability in the S =1 Bose-Hubbard model
Asaoka, Rui; Tsuchiura, Hiroki; Yamashita, Makoto; Toga, Yuta
2016-01-01
We study the dynamical instabilities of superfluid flows in the S =1 Bose-Hubbard model. The time evolution of each spin component in a condensate is calculated based on the dynamical Gutzwiller approximation for a wide range of interactions, from a weakly correlated regime to a strongly correlated regime near the Mott-insulator transition. Owing to the spin-dependent interactions, the superfluid flow of the spin-1 condensate decays at a different critical momentum from a spinless case when the interaction strength is the same. We furthermore calculate the dynamical phase diagram of this model and clarify that the obtained phase boundary has very different features depending on whether the average number of particles per site is even or odd. Finally, we analyze the density and spin modulations that appear in association with the dynamical instability. We find that spin modulations are highly sensitive to the presence of a uniform magnetic field.
Phase transitions in the Hubbard model for the bismuth nickelate
Kojima, Shoya; Nasu, Joji; Koga, Akihisa
2016-07-01
We study low temperature properties of the Hubbard model for the bismuth nickelate, where degenerate orbitals in the nickel ions and a single orbital in the bismuth ions are taken into account, combining dynamical mean-field theory with the continuous-time quantum Monte Carlo method. We discuss the effect of the attractive interactions to mimic the valence skipping phenomenon in the bismuth ions. We demonstrate how the charge and magnetically ordered states are stable against thermal fluctuations. It is furthermore clarified that the ferromagnetically ordered and orbital ordered states are stabilized due to the presence of the orbital degeneracy at low temperatures. The crossover between metallic and insulating states is also discussed.
Functional renormalization for antiferromagnetism and superconductivity in the Hubbard model
Results of a renormalization group study for the 2-dimensional Hubbard model close to half-filling at finite temperature are presented. Bosonic degrees of freedom corresponding to antiferromagnetic and d-wave superconducting order are introduced, and flow equations for the corresponding coupling constants are deduced from an exact flow equation for the effective average action. The influence of bosonic fluctuations on the onset of local antiferromagnetic order is discussed. At low enough temperatures and close to half-filling the discrete symmetry of the lattice is broken and incommensurate antiferromagnetic fluctuations dominate. The phase diagram is shown for the parameter regime close to half-filling in the presence of vanishing as well as non-vanishing next-to-nearest-neighbor hopping t'. Finally, the potential emergence of d-wave superconducting order at larger distances from half-filling is discussed.
One-dimensional Hubbard-Luttinger model for carbon nanotubes
Ishkhanyan, H. A.; Krainov, V. P.
2015-06-01
A Hubbard-Luttinger model is developed for qualitative description of one-dimensional motion of interacting Pi-conductivity-electrons in carbon single-wall nanotubes at low temperatures. The low-lying excitations in one-dimensional electron gas are described in terms of interacting bosons. The Bogolyubov transformation allows one to describe the system as an ensemble of non-interacting quasi-bosons. Operators of Fermi excitations and Green functions of fermions are introduced. The electric current is derived as a function of potential difference on the contact between a nanotube and a normal metal. Deviations from Ohm law produced by electron-electron short-range repulsion as well as by the transverse quantization in single-wall nanotubes are discussed. The results are compared with experimental data.
Conductivite dans le modele de Hubbard bi-dimensionnel a faible couplage
Bergeron, Dominic
Le modele de Hubbard bi-dimensionnel (2D) est souvent considere comme le modele minimal pour les supraconducteurs a haute temperature critique a base d'oxyde de cuivre (SCHT). Sur un reseau carre, ce modele possede les phases qui sont communes a tous les SCHT, la phase antiferromagnetique, la phase supraconductrice et la phase dite du pseudogap. Il n'a pas de solution exacte, toutefois, plusieurs methodes approximatives permettent d'etudier ses proprietes de facon numerique. Les proprietes optiques et de transport sont bien connues dans les SCHT et sont donc de bonne candidates pour valider un modele theorique et aider a comprendre mieux la physique de ces materiaux. La presente these porte sur le calcul de ces proprietes pour le modele de Hubbard 2D a couplage faible ou intermediaire. La methode de calcul utilisee est l'approche auto-coherente a deux particules (ACDP), qui est non-perturbative et inclue l'effet des fluctuations de spin et de charge a toutes les longueurs d'onde. La derivation complete de l'expression de la conductivite dans l'approche ACDP est presentee. Cette expression contient ce qu'on appelle les corrections de vertex, qui tiennent compte des correlations entre quasi-particules. Pour rendre possible le calcul numerique de ces corrections, des algorithmes utilisant, entre autres, des transformees de Fourier rapides et des splines cubiques sont developpes. Les calculs sont faits pour le reseau carre avec sauts aux plus proches voisins autour du point critique antiferromagnetique. Aux dopages plus faibles que le point critique, la conductivite optique presente une bosse dans l'infrarouge moyen a basse temperature, tel qu'observe dans plusieurs SCHT. Dans la resistivite en fonction de la temperature, on trouve un comportement isolant dans le pseudogap lorsque les corrections de vertex sont negligees et metallique lorsqu'elles sont prises en compte. Pres du point critique, la resistivite est lineaire en T a basse temperature et devient
Fermi hyper-netted chain theory on a lattice: The Hubbard model
We review a new lattice version of Fermi Hyper-Netted Chain method for the study of strongly interacting electrons. The ordinary paramagnetic and the spin density wave functions have been correlated with Jastrow-type and e-d correlations, and the corresponding FHNC equations for the pair distribution function, the one body density matrix and the staggered magnetization are discussed. Results for the 1D chain and 2D square lattice models are presented and compared with the available results obtained within Quantum Monte Carlo, variational Monte Carlo and exact diagonalization of a 4x4 Hubbard cluster. Particularly interesting are the strong effects of e-d correlations on E/Nt and on the momentum distribution as well as antiferromagnetic behavior away from half filling found in our FHNC calculations in agreement with other studies. (author). 35 refs, 8 figs, 2 tabs
Bracken, Anthony J.; Ge Xiangyu; Gould, Mark D.; Links, Jon; Zhou Huanqiang [Centre for Mathematical Physics, University of Queensland, Brisbane, QLD (Australia)
2001-06-01
Integrable extended Hubbard models arising from symmetric group solutions are examined in the framework of the graded quantum inverse scattering method. The Bethe ansatz equations for all these models are derived by using the algebraic Bethe ansatz method. (author)
Dynamical Model and Path Integral Formalism for Hubbard Operators
Foussats, A.; Greco, A. (Anna); Zandron, O. S.
1998-01-01
In this paper, the possibility to construct a path integral formalism by using the Hubbard operators as field dynamical variables is investigated. By means of arguments coming from the Faddeev-Jackiw symplectic Lagrangian formalism as well as from the Hamiltonian Dirac method, it can be shown that it is not possible to define a classical dynamics consistent with the full algebra of the Hubbard $X$-operators. Moreover, from the Faddeev-Jackiw symplectic algorithm, and in order to satisfy the H...
Antiferromagnetism and d-wave superconductivity in the Hubbard model
The two-dimensional Hubbard model is a promising effective model for the electronic degrees of freedom in the copper-oxide planes of high temperature superconductors. We present a functional renormalization group approach to this model with focus on antiferromagnetism and d-wave superconductivity. In order to make the relevant degrees of freedom more explicitly accessible on all length scales, we introduce composite bosonic fields mediating the interaction between the fermions. Spontaneous symmetry breaking is reflected in a non-vanishing expectation value of a bosonic field. The emergence of a coupling in the d-wave pairing channel triggered by spin wave fluctuations is demonstrated. Furthermore, the highest temperature at which the interaction strength for the electrons diverges in the renormalization flow is calculated for both antiferromagnetism and d-wave superconductivity over a wide range of doping. This ''pseudo-critical'' temperature signals the onset of local ordering. Moreover, the temperature dependence of d-wave superconducting order is studied within a simplified model characterized by a single coupling in the d-wave pairing channel. The phase transition within this model is found to be of the Kosterlitz-Thouless type. (orig.)
Antiferromagnetism and d-wave superconductivity in the Hubbard model
Krahl, H.C.
2007-07-25
The two-dimensional Hubbard model is a promising effective model for the electronic degrees of freedom in the copper-oxide planes of high temperature superconductors. We present a functional renormalization group approach to this model with focus on antiferromagnetism and d-wave superconductivity. In order to make the relevant degrees of freedom more explicitly accessible on all length scales, we introduce composite bosonic fields mediating the interaction between the fermions. Spontaneous symmetry breaking is reflected in a non-vanishing expectation value of a bosonic field. The emergence of a coupling in the d-wave pairing channel triggered by spin wave fluctuations is demonstrated. Furthermore, the highest temperature at which the interaction strength for the electrons diverges in the renormalization flow is calculated for both antiferromagnetism and d-wave superconductivity over a wide range of doping. This ''pseudo-critical'' temperature signals the onset of local ordering. Moreover, the temperature dependence of d-wave superconducting order is studied within a simplified model characterized by a single coupling in the d-wave pairing channel. The phase transition within this model is found to be of the Kosterlitz-Thouless type. (orig.)
Ising tricriticality in the extended Hubbard model with bond dimerization
Ejima, Satoshi; Essler, Fabian H. L.; Lange, Florian; Fehske, Holger
2016-06-01
We explore the quantum phase transition between Peierls and charge-density-wave insulating states in the one-dimensional, half-filled, extended Hubbard model with explicit bond dimerization. We show that the critical line of the continuous Ising transition terminates at a tricritical point, belonging to the universality class of the tricritical Ising model with central charge c =7 /10 . Above this point, the quantum phase transition becomes first order. Employing a numerical matrix-product-state based (infinite) density-matrix renormalization group method we determine the ground-state phase diagram, the spin and two-particle charge excitations gaps, and the entanglement properties of the model with high precision. Performing a bosonization analysis we can derive a field description of the transition region in terms of a triple sine-Gordon model. This allows us to derive field theory predictions for the power-law (exponential) decay of the density-density (spin-spin) and bond-order-wave correlation functions, which are found to be in excellent agreement with our numerical results.
Exact solution of a new class of Hubbard-type models with open boundary conditions
A new class of Hubbard-type models with open boundary conditions in one dimension is studied in the framework of coordinate Bethe ansatz method. The energy spectrum, integrable boundary conditions and the corresponding Bethe ansatz equations are derived. (authors)
Phase diagram of the half-filled ionic Hubbard model
Bag, Soumen; Garg, Arti; Krishnamurthy, H. R.
2015-06-01
We study the phase diagram of the ionic Hubbard model (IHM) at half filling on a Bethe lattice of infinite connectivity using dynamical mean-field theory (DMFT), with two impurity solvers, namely, iterated perturbation theory (IPT) and continuous time quantum Monte Carlo (CTQMC). The physics of the IHM is governed by the competition between the staggered ionic potential Δ and the on-site Hubbard U . We find that for a finite Δ and at zero temperature, long-range antiferromagnetic (AFM) order sets in beyond a threshold U =UA F via a first-order phase transition. For U smaller than UA F the system is a correlated band insulator. Both methods show a clear evidence for a quantum transition to a half-metal (HM) phase just after the AFM order is turned on, followed by the formation of an AFM insulator on further increasing U . We show that the results obtained within both methods have good qualitative and quantitative consistency in the intermediate-to-strong-coupling regime at zero temperature as well as at finite temperature. On increasing the temperature, the AFM order is lost via a first-order phase transition at a transition temperature TA F(U ,Δ ) [or, equivalently, on decreasing U below UA F(T ,Δ ) ], within both methods, for weak to intermediate values of U /t . In the strongly correlated regime, where the effective low-energy Hamiltonian is the Heisenberg model, IPT is unable to capture the thermal (Neel) transition from the AFM phase to the paramagnetic phase, but the CTQMC does. At a finite temperature T , DMFT +CTQMC shows a second phase transition (not seen within DMFT +IPT ) on increasing U beyond UA F. At UN>UA F , when the Neel temperature TN for the effective Heisenberg model becomes lower than T , the AFM order is lost via a second-order transition. For U ≫Δ , TN˜t2/U (1 -x2) , where x =2 Δ /U and thus TN increases with increase in Δ /U . In the three-dimensional parameter space of (U /t ,T /t ,andΔ /t ) , as T increases, the surface of first
Time-of-flight images of Mott insulators in the Hofstadter- Bose-Hubbard model
Işkın, Menderes
2015-01-01
PHYSICAL REVIEW A 92, 023636 (2015) Time-of-flight images of Mott insulators in the Hofstadter-Bose-Hubbard model M. Iskin Department of Physics, Koc¸ University, Rumelifeneri Yolu, 34450 Sarıyer, Istanbul, Turkey (Received 10 April 2015; published 26 August 2015) We analyze the momentum distribution function and its artificial-gauge-field dependence for theMott insulator phases of the Hofstadter-Bose-Hubbard model. By benchmarking the results of the random-phase approximati...
Diffusion dynamics in the disordered Bose Hubbard model
Wadleigh, Laura; Russ, Philip; Demarco, Brian
2016-05-01
We explore the dynamics of diffusion for out-of-equilibrium superfluid, Mott insulator, and Bose glass states using an atomic realization of the disordered Bose Hubbard (DBH) model. Dynamics in strongly correlated systems, especially far from equilibrium, are not well understood. The introduction of disorder further complicates these systems. We realize the DBH model--which has been central to our understanding of quantum phase transitions in disordered systems--using ultracold Rubidium-87 atoms trapped in a cubic disordered optical lattice. By tightly focusing a beam into the center of the gas, we create a hole in the atomic density profile. We achieve Mott insulator, superfluid, or Bose glass states by varying the interaction and disorder strength, and measure the time evolution of the density profile after removing the central barrier. This allows us to infer diffusion rates from the velocities at the edge of the hole and to look for signatures of superfluid puddles in the Bose glass state. We acknowledge funding from NSF Grant PHY 15-05468, NSF Grant DGE-1144245, and ARO Grant W911NF-12-1-0462.
Exact solutions of the high dimensional hard-core Fermi-Hubbard model
PAN; Feng
2001-01-01
［1］Hubbard, J., Electron correlations in narrow energy bands, Proc. R. Soc. London, A, 963, 276: 238.［2］Hubbard, J., Electron correlations in narrow energy bands II. The degenerate band case, Proc. R. Soc. London A, 963, A277: 237.［3］Anderson, P. W., The resonating valence bond state in La2CuOand superconductivity, Science, 987, 235: 96.［4］Lieb, E. H, Wu, F. Y., Absence of Mott transition in an exact solution of the short-range one-band model in one dimension, Phys. Rev. Lett., 968, 20: 445.［5］Ogata, M., Shiba, H., Bethe-ansatz wave function, momentum distribution, and spin correlation in the one-dimensional strongly correlated Hubbard model, Phys. Rev., 990, B4: 326.［6］Ogata, M., Sugiyama, T., Shiba, H., Magnetic-field effects on the correlation functions in the one-dimensional strongly correlated Hubbard model, Phys. Rev., 990, B43: 840.［7］Mei, C., Chen, L., Study of the interaction between two electrons in the single band Hubbard model, Z. Phys., 988, B72: 429.［8］Caspers, W. J., Iske, P. L., Exact spectrum for n electrons in the single band Hubbard model, Physica, 989, A, 57: 033.［9］Kirson, M. W., A dynamical supersymmetry in the Hubbard model, Phys. Rev. Lett., 997, 78: 24.［10］Woynarovich, F., Excitations with complex wavefunctions in a Hubbard chain: II. States with several pairs of complex wavenumbers, J. Phys., 982, C5: 97.
Ground state of the three-band Hubbard model
Yanagisawa, Takashi; Koike, Soh; Yamaji, Kunihiko
2001-11-01
The ground state of the two-dimensional three-band Hubbard model in oxide superconductors is investigated by using the variational Monte Carlo method. The Gutzwiller-projected BCS and spin density wave (SDW) functions are employed in the search for a possible ground state with respect to dependences on electron density. Antiferromagnetic correlations are considerably strong near half-filling. It is shown that the d-wave state may exist away from half-filling for both the hole and electron doping cases. The overall structure of the phase diagram obtained by our calculations qualitatively agrees with experimental indications. The superconducting condensation energy is in reasonable agreement with the experimental value obtained from specific heat and critical magnetic field measurements for optimally doped samples. The inhomogeneous SDW state is also examined near 1/8 doping. Incommensurate magnetic structures become stable due to hole doping in the underdoped region, where the transfer tpp between oxygen orbitals plays an important role in determining a stable stripe structure.
Attractive Hubbard model: Homogeneous Ginzburg-Landau expansion and disorder
Kuchinskii, E. Z.; Kuleeva, N. A.; Sadovskii, M. V.
2016-02-01
We derive a Ginzburg-Landau (GL) expansion in the disordered attractive Hubbard model within the combined Nozieres-Schmitt-Rink and DMFT+Σ approximation. Restricting ourselves to the homogeneous expansion, we analyze the disorder dependence of GL expansion coefficients for a wide range of attractive potentials U, from the weak BCS coupling region to the strong-coupling limit, where superconductivity is described by Bose-Einstein condensation (BEC) of preformed Cooper pairs. We show that for the a semielliptic "bare" density of states of the conduction band, the disorder influence on the GL coefficients A and B before quadratic and quartic terms of the order parameter, as well as on the specific heat discontinuity at the superconducting transition, is of a universal nature at any strength of the attractive interaction and is related only to the general widening of the conduction band by disorder. In general, disorder growth increases the values of the coefficients A and B, leading either to a suppression of the specific heat discontinuity (in the weak-coupling limit), or to its significant growth (in the strong-coupling region). However, this behavior actually confirms the validity of the generalized Anderson theorem, because the disorder dependence of the superconducting transition temperature T c, is also controlled only by disorder widening of the conduction band (density of states).
2-D Model Test of Dolosse Breakwater
Burcharth, Hans F.; Liu, Zhou
1994-01-01
The rational design diagram for Dolos armour should incorporate both the hydraulic stability and the structural integrity. The previous tests performed by Aalborg University (AU) made available such design diagram for the trunk of Dolos breakwater without superstructures (Burcharth et al. 1992). To...... extend the design diagram to cover Dolos breakwaters with superstructure, 2-D model tests of Dolos breakwater with wave wall is included in the project Rubble Mound Breakwater Failure Modes sponsored by the Directorate General XII of the Commission of the European Communities under Contract MAS-CT92......-0042. Furthermore, Task IA will give the design diagram for Tetrapod breakwaters without a superstructure. The more complete research results on Dolosse can certainly give some insight into the behaviour of Tetrapods armour layer of the breakwaters with superstructure. The main part of the experiment was on the...
Attractive Hubbard model with disorder and the generalized Anderson theorem
Using the generalized DMFT+Σ approach, we study the influence of disorder on single-particle properties of the normal phase and the superconducting transition temperature in the attractive Hubbard model. A wide range of attractive potentials U is studied, from the weak coupling region, where both the instability of the normal phase and superconductivity are well described by the BCS model, to the strong-coupling region, where the superconducting transition is due to Bose-Einstein condensation (BEC) of compact Cooper pairs, formed at temperatures much higher than the superconducting transition temperature. We study two typical models of the conduction band with semi-elliptic and flat densities of states, respectively appropriate for three-dimensional and two-dimensional systems. For the semi-elliptic density of states, the disorder influence on all single-particle properties (e.g., density of states) is universal for an arbitrary strength of electronic correlations and disorder and is due to only the general disorder widening of the conduction band. In the case of a flat density of states, universality is absent in the general case, but still the disorder influence is mainly due to band widening, and the universal behavior is restored for large enough disorder. Using the combination of DMFT+Σ and Nozieres-Schmitt-Rink approximations, we study the disorder influence on the superconducting transition temperature Tc for a range of characteristic values of U and disorder, including the BCS-BEC crossover region and the limit of strong-coupling. Disorder can either suppress Tc (in the weak-coupling region) or significantly increase Tc (in the strong-coupling region). However, in all cases, the generalized Anderson theorem is valid and all changes of the superconducting critical temperature are essentially due to only the general disorder widening of the conduction band
Surface modelling for 2D imagery
Lieng, Henrik
2014-01-01
Vector graphics provides powerful tools for drawing scalable 2D imagery. With the rise of mobile computers, of different types of displays and image resolutions, vector graphics is receiving an increasing amount of attention. However, vector graphics is not the leading framework for creating and manipulating 2D imagery. The reason for this reluctance of employing vector graphical frameworks is that it is difficult to handle complex behaviour of colour across the 2D domain. ...
Quantum simulation of the Hubbard model with dopant atoms in silicon
Salfi, J.; Mol, J. A.; Rahman, R.; Klimeck, G.; Simmons, M. Y.; Hollenberg, L. C. L.; Rogge, S.
2016-04-01
In quantum simulation, many-body phenomena are probed in controllable quantum systems. Recently, simulation of Bose-Hubbard Hamiltonians using cold atoms revealed previously hidden local correlations. However, fermionic many-body Hubbard phenomena such as unconventional superconductivity and spin liquids are more difficult to simulate using cold atoms. To date the required single-site measurements and cooling remain problematic, while only ensemble measurements have been achieved. Here we simulate a two-site Hubbard Hamiltonian at low effective temperatures with single-site resolution using subsurface dopants in silicon. We measure quasi-particle tunnelling maps of spin-resolved states with atomic resolution, finding interference processes from which the entanglement entropy and Hubbard interactions are quantified. Entanglement, determined by spin and orbital degrees of freedom, increases with increasing valence bond length. We find separation-tunable Hubbard interaction strengths that are suitable for simulating strongly correlated phenomena in larger arrays of dopants, establishing dopants as a platform for quantum simulation of the Hubbard model.
Modelling one-dimensional insulating materials with the ionic Hubbard model
The single-particle spectral-weight function of the ionic Hubbard model (IHM) at half-filling shows an abrupt change of regime at a critical value of the coupling constant (Hubbard U). Specifically, this function jumps at the Fermi points kF = ± π/2 from a two-peak to a four-peak structure accompanied by a (non-vanishing) minimum of the single-particle charge gap. This jump separates a weak-coupling regime, the band insulating phase, from a strong-coupling regime which evolves gradually into the Mott-Hubbard phase. We take advantage of this critical behaviour to model several quasi-one-dimensional materials in terms of the IHM instead of the simpler one-band Hubbard model. For instance, the two regimes are physically realized in the angle-resolved photoelectron spectra of (TaSe4)2I, and the blue-bronze K0.3MoO3, respectively
Energy of ground state in B-B'-U-Hubbard model in approximation of static fluctuations
Mironov, G I
2002-01-01
To explain some features of CuO sub 2 base high-temperature superconductors (HTSC) one should take account of possibility of electron transfer to the crystalline structure mode next to the nearest one. It terms of approximation of static fluctuations one calculated the energy of ground state in two-dimensional B-B'-U Hubbard model. Lattice is assumed to consist of two sublattices formed by various type atoms. The calculation results of ground state energy are compared with the precise solution for one-dimensional Hubbard model derived previously. Comparison of the precise and the approximated solutions shows that approximation of static fluctuations describes adequately behavior of the Hubbard studied model within both weak and strong correlation ranges
Density-dependent tunneling in the extended Bose–Hubbard model
Recently, it has become apparent that when the interactions between polar molecules in optical lattices become strong, the conventional description using the extended Hubbard model has to be modified by additional terms, in particular a density-dependent tunneling term. We investigate here the influence of this term on the ground-state phase diagrams of the two-dimensional extended Bose–Hubbard model. Using quantum Monte Carlo simulations, we investigate the changes of the superfluid, supersolid and phase-separated parameter regions in the phase diagram of the system. By studying the interplay of the density-dependent hopping with the usual on-site interaction U and nearest-neighbor repulsion V , we show that the ground-state phase diagrams differ significantly from those expected from the standard extended Bose–Hubbard model. (paper)
Density-dependent tunneling in the extended Bose-Hubbard model
Maik, Michał; Hauke, Philipp; Dutta, Omjyoti; Lewenstein, Maciej; Zakrzewski, Jakub
2013-11-01
Recently, it has become apparent that when the interactions between polar molecules in optical lattices become strong, the conventional description using the extended Hubbard model has to be modified by additional terms, in particular a density-dependent tunneling term. We investigate here the influence of this term on the ground-state phase diagrams of the two-dimensional extended Bose-Hubbard model. Using quantum Monte Carlo simulations, we investigate the changes of the superfluid, supersolid and phase-separated parameter regions in the phase diagram of the system. By studying the interplay of the density-dependent hopping with the usual on-site interaction U and nearest-neighbor repulsion V , we show that the ground-state phase diagrams differ significantly from those expected from the standard extended Bose-Hubbard model.
Density of States for Hubbard and Emery Model from an Interpolated Self Energy
A Green s Function technique interpolating the self energy between second order perturbation theory and the atomic limit is applied to correlated models. In the doped one band Hubbard model the chemical potential passes a Kondo like resonance, in the three band model it passes the maximum of a correlation induced singlet band. (author)
Coe, J P; D' Amico, I [Department of Physics, University of York, York YO10 5DD (United Kingdom); Franca, V V, E-mail: jpc503@york.ac.uk, E-mail: vivian.franca@physik.uni-freiburg.de, E-mail: ida500@york.ac.uk [Physikalisches Institut, Albert-Ludwigs-Universitaet, Hermann-Herder-Strasse 3, D-79104 Freiburg (Germany)
2011-07-06
We consider the position-space information and linear entropies as proxy measures to the average single-site entanglement-quantified using the von Neumann entropy-of the one-dimensional Hubbard model and of a one-dimensional nanostructure system comprised of an array of quantum-dots. Spatial entanglement in the quantum-dot system is also investigated via the three entropies. We appraise the use of the possible proxy measures in the Hubbard model as an approximation to their use for the nanostructure system.
Afchain, St
2005-02-15
The Hubbard model is the simplest model to describe the behaviour of fermions on a network, it takes into account only fermion scattering and only interactions with other fermions located on the same site. Half-filling means that the total number of fermions is equal to half the number of sites. In the first chapter we show how we can pass trough successive approximations from a very general Hamiltonian to the Hubbard Hamiltonian. The second chapter is dedicated to the passage from the Hamiltonian formalism to the Grassmanian functional formalism. The main idea is to show that the correlation functions of the Hamiltonian approach can be described through fermionic functional integrals which implies the possibility of speaking of the model in terms of field theory. The chapter 3 deals with the main constructive techniques that allow the strict and consistent construction of models inside the frame of field theory. We show by proving the violation of a condition concerning self-energy, that the two-dimensional Hubbard model at half-filling has not the behaviour of a Fermi liquid in the Landau's interpretation. (A.C.)
Metal-insulator transition in three-band Hubbard model
We describe a transition from a metal to an antiferromagnetic (AF) insulator in the three-band Hubbard Hamiltonian for the undoped CuO2 planes of high-temperature superconductors, including local hole correlations. If the realistic parameters are used, one finds the AF ground states with magnetic moment of ≅0.47μB and ≅0.56μB for La2CuO4 and YBa2Cu2O6, respectively. Correlations and the interoxygen hopping reduce drastically the region of the AF long-range order which disappears for the doping of 0.06 hole per unit cell. (orig.)
Classical mapping for Hubbard operators: Application to the double-Anderson model
Li, Bin; Miller, William H. [Department of Chemistry and Kenneth S. Pitzer Center for Theoretical Chemistry, University of California, and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States); Levy, Tal J.; Rabani, Eran [School of Chemistry, The Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978 (Israel)
2014-05-28
A classical Cartesian mapping for Hubbard operators is developed to describe the nonequilibrium transport of an open quantum system with many electrons. The mapping of the Hubbard operators representing the many-body Hamiltonian is derived by using analogies from classical mappings of boson creation and annihilation operators vis-à-vis a coherent state representation. The approach provides qualitative results for a double quantum dot array (double Anderson impurity model) coupled to fermionic leads for a range of bias voltages, Coulomb couplings, and hopping terms. While the width and height of the conduction peaks show deviations from the master equation approach considered to be accurate in the limit of weak system-leads couplings and high temperatures, the Hubbard mapping captures all transport channels involving transition between many electron states, some of which are not captured by approximate nonequilibrium Green function closures.
Phase diagram of the Hubbard model with arbitrary band filling: renormalization group approach
The finite temperature phase diagram of the Hubbard model in d = 2 and d = 3 is calculated for arbitrary values of the parameter U/t and chemical potential μ using a quantum real space renormalization group. Evidence for a ferromagnetic phase at low temperatures is presented. (author). 15 refs., 5 figs
Phase diagram of exciton condensate in doped two-band Hubbard model
Kuneš, Jan
2014-01-01
Roč. 90, č. 23 (2014), "235140-1"-"235140-8". ISSN 1098-0121 R&D Projects: GA ČR GA13-25251S Institutional support: RVO:68378271 Keywords : Hubbard model * spin-state transition * semiconductor-semimetal transition Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.736, year: 2014
Relative and center-of-mass motion in the attractive Bose-Hubbard model
Sørensen, Ole Søe; Gammelmark, Søren; Mølmer, Klaus
2012-01-01
We present first-principles numerical calculations for few-particle solutions of the attractive Bose-Hubbard model with periodic boundary conditions. We show that the low-energy many-body states found by numerical diagonalization can be written as translational superposition states of compact...
Numerical studies of ground-state fidelity of the Bose-Hubbard model
ŁÄ cki, Mateusz; Damski, Bogdan; Zakrzewski, Jakub
2014-03-01
We compute ground-state fidelity of the one-dimensional Bose-Hubbard model at unit filling factor. To this aim, we apply the density matrix renormalization group algorithm to systems with open and periodic boundary conditions. We find that fidelity differs significantly in the two cases and study its scaling properties in the quantum critical regime.
Metal-insulator transition in three-band Hubbard model
Dutka, J.; Kaminski, M. (Inst. of Physics, Jagiellonian Univ., Cracow (Poland)); Oles, A.M. (Inst. of Physics, Jagiellonian Univ., Cracow (Poland) Max-Planck-Inst., FKF, Stuttgart (Germany))
1992-02-01
We describe a transition from a metal to an antiferromagnetic (AF) insulator in the three-band Hubbard Hamiltonian for the undoped CuO{sub 2} planes of high-temperature superconductors, including local hole correlations. If the realistic parameters are used, one finds the AF ground states with magnetic moment of {approx equal}0.47{mu}{sub B} and {approx equal}0.56{mu}{sub B} for La{sub 2}CuO{sub 4} and YBa{sub 2}Cu{sub 2}O{sub 6}, respectively. Correlations and the interoxygen hopping reduce drastically the region of the AF long-range order which disappears for the doping of 0.06 hole per unit cell. (orig.).
Fermion spectrum of Bose-Fermi-Hubbard model in the phase with Bose-Einstein condensate
We investigate the fermion spectrum within the Bose- Fermi-Hubbard model used for the description of boson-fermion mixtures of ultra-cold atoms in optical lattices. We used the method based on the Hubbard operator approach for an on-site basis. The equation for fermion Green's function in the Bose-Fermi-Hubbard model is built; Green's functions of higher orders are decoupled in the Hubbard-I approximation (the case of the strong on-site interaction). The corresponding spectral densities are calculated. In the case of hard-core bosons, the condition of appearance of additional bands in the fermion spectrum is investigated. It is shown that these bands exist only in the state with a Bose- Einstein condensate and appear because of the mixing of states with different numbers of bosons. These additional bands can be interpreted as a manifestation of composite excitations (when the appearance of a fermion on the site is accompanied by the simultaneous creation (or annihilation) of a boson)
Symmetries and solvable models for evaporating 2D black holes
Cruz Muñoz, José Luis; Navarro-Salas, José; Navarro Navarro, Miguel; Talavera, C. F.
1997-01-01
We study the evaporation process of a 2D black hole in thermal equilibrium when the ingoing radiation is suddenly switched off. We also introduce global symmetries of generic 2D dilaton gravity models which generalize the extra symmetry of the CGHS model. © Elsevier Science B.V
Maximizing entropy of image models for 2-D constrained coding
Forchhammer, Søren; Danieli, Matteo; Burini, Nino; Zamarin, Marco; Ukhanova, Ann
2010-01-01
This paper considers estimating and maximizing the entropy of two-dimensional (2-D) fields with application to 2-D constrained coding. We consider Markov random fields (MRF), which have a non-causal description, and the special case of Pickard random fields (PRF). The PRF are 2-D causal finite context models, which define stationary probability distributions on finite rectangles and thus allow for calculation of the entropy. We consider two binary constraints and revisit the hard square const...
Universal Quantum Computation by Scattering in the Fermi-Hubbard Model
Bao, Ning; Salton, Grant; Thomas, Nathaniel
2014-01-01
The Hubbard model may be the simplest model of particles interacting on a lattice, but simulation of its dynamics remains beyond the reach of current numerical methods. In this article, we show that general quantum computations can be encoded into the physics of wave packets propagating through a planar graph, with scattering interactions governed by the fermionic Hubbard model. Therefore, simulating the model on planar graphs is as hard as simulating quantum computation. We give two different arguments, demonstrating that the simulation is difficult both for wave packets prepared as excitations of the fermionic vacuum, and for hole wave packets at filling fraction one-half in the limit of strong coupling. In the latter case, which is described by the t-J model, there is only reflection and no transmission in the scattering events, as would be the case for classical hard spheres. In that sense, the construction provides a quantum mechanical analog of the Fredkin-Toffoli billiard ball computer.
Competing interactions and symmetry breaking in the Hubbard-Holstein model
Bauer, Johannes
2009-01-01
Competing interactions are often responsible for intriguing phase diagrams in correlated electron systems. Here we analyze the competition of instantaneous short range Coulomb interaction $U$ with the retarded electron-electron interaction induced by an electron-phonon coupling $g$ as described by the Hubbard-Holstein model. The ground state phase diagram of this model in the limit of large dimensions at half filling is established. The study is based on dynamical mean field theory combined w...
Orientational bond and N\\'eel order in the two-dimensional ionic Hubbard model
Hafez-Torbati, Mohsen; Uhrig, Götz S.
2015-01-01
Unconventional phases often occur where two competing mechanisms compensate. An excellent example is the ionic Hubbard model where the alternating local potential $\\delta$, favoring a band insulator (BI), competes with the local repulsion $U$, favoring a Mott insulator (MI). By continuous unitary transformations we derive effective models in which we study the softening of various excitons. The softening signals the instability towards new phases that we describe on the mean-field level. On i...
Class of variational singlet wave functions for the Hubbard model away from half filling
We present a class of variational wave functions for strong-coupling Heisenberg Hubbard models. These are written in the form of three factors---a pair of determinants and a Jastrow function---and are made out of orbitals, a la Hartree-Fock theory, which solve a fictitious one-body problem. The wave functions respect various constraints known from general principles and appear to be potentially useful in understanding the possible behavior of the models in quantitative terms
Edge superconducting state in attractive U Kane-Mele-Hubbard model
Yuan, J.; Gao, JH; Chen, WQ; Ye, F; Zhou, Y.; Zhang, FC
2012-01-01
We theoretically investigate the phase transition from topological insulator (TI) to superconductor in the attractive U Kane-Mele-Hubbard model with self-consistent mean field method. We demonstrate the existence of edge superconducting state (ESS), in which the bulk is still an insulator and the superconductivity only appears near the edges. The ESS results from the special energy dispersion of TI, and is a general property of the superconductivity in TI. The phase transition in this model e...
Effective electron-electron and electron-phonon interactions in the Hubbard-Holstein model
Aprea, G; Di Castro, C.; Grilli, M.; Lorenzana, J.
2006-01-01
We investigate the interplay between the electron-electron and the electron-phonon interaction in the Hubbard-Holstein model. We implement the flow-equation method to investigate within this model the effect of correlation on the electron-phonon effective coupling and, conversely, the effect of phonons in the effective electron-electron interaction. Using this technique we obtain analytical momentum-dependent expressions for the effective couplings and we study their behavior for different ph...
Kalman Filter for Generalized 2-D Roesser Models
SHENG Mei; ZOU Yun
2007-01-01
The design problem of the state filter for the generalized stochastic 2-D Roesser models, which appears when both the state and measurement are simultaneously subjected to the interference from white noise, is discussed. The wellknown Kalman filter design is extended to the generalized 2-D Roesser models. Based on the method of "scanning line by line", the filtering problem of generalized 2-D Roesser models with mode-energy reconstruction is solved. The formula of the optimal filtering, which minimizes the variance of the estimation error of the state vectors, is derived. The validity of the designed filter is verified by the calculation steps and the examples are introduced.
Study of the two-dimensional Hubbard model at half-filling through constructive methods
The Hubbard model is the simplest model to describe the behaviour of fermions on a network, it takes into account only fermion scattering and only interactions with other fermions located on the same site. Half-filling means that the total number of fermions is equal to half the number of sites. In the first chapter we show how we can pass trough successive approximations from a very general Hamiltonian to the Hubbard Hamiltonian. The second chapter is dedicated to the passage from the Hamiltonian formalism to the Grassmanian functional formalism. The main idea is to show that the correlation functions of the Hamiltonian approach can be described through fermionic functional integrals which implies the possibility of speaking of the model in terms of field theory. The chapter 3 deals with the main constructive techniques that allow the strict and consistent construction of models inside the frame of field theory. We show by proving the violation of a condition concerning self-energy, that the two-dimensional Hubbard model at half-filling has not the behaviour of a Fermi liquid in the Landau's interpretation. (A.C.)
Silant’ev, A. V., E-mail: kvvant@rambler.ru [Mari State University (Russian Federation)
2015-10-15
Anticommutator Green’s functions and the energy spectrum of C{sub 60} fullerene are calculated in the approximation of static fluctuations within the Hubbard model. On the basis of this spectrum, an interpretation is proposed for the experimentally observed optical absorption bands of C{sub 60} fullerene. The parameters of C{sub 60} fullerene that characterize it within the Hubbard model are calculated by the optical absorption spectrum.
Detecting phase transitions and crossovers in Hubbard models using the fidelity susceptibility
Huang, Li; Wang, Lei; Werner, Philipp
2016-01-01
A generalized version of the fidelity susceptibility of single-band and multi-orbital Hubbard models is systematically studied using single-site dynamical mean-field theory in combination with a hybridization expansion continuous-time quantum Monte Carlo impurity solver. We find that the fidelity susceptibility is extremely sensitive to changes in the state of the system. It can be used as a numerically inexpensive tool to detect and characterize a broad range of phase transitions and crossovers in Hubbard models, including (orbital-selective) Mott metal-insulator transitions, high-spin to low-spin transitions, Fermi-liquid to non-Fermi-liquid crossovers, and spin-freezing crossovers.
Doping evolution of spin and charge excitations in the Hubbard model
Kung, YF; Nowadnick, EA; Jia, CJ; Johnston, S.; B. Moritz; Scalettar, RT; Devereaux, TP
2015-01-01
© 2015 American Physical Society. To shed light on how electronic correlations vary across the phase diagram of the cuprate superconductors, we examine the doping evolution of spin and charge excitations in the single-band Hubbard model using determinant quantum Monte Carlo (DQMC). In the single-particle response, we observe that the effects of correlations weaken rapidly with doping, such that one may expect the random phase approximation (RPA) to provide an adequate description of the two-p...
Coexistence of Incommensurate Magnetism and Superconductivity in the Two-Dimensional Hubbard Model.
Yamase, Hiroyuki; Eberlein, Andreas; Metzner, Walter
2016-03-01
We analyze the competition of magnetism and superconductivity in the two-dimensional Hubbard model with a moderate interaction strength, including the possibility of incommensurate spiral magnetic order. Using an unbiased renormalization group approach, we compute magnetic and superconducting order parameters in the ground state. In addition to previously established regions of Néel order coexisting with d-wave superconductivity, the calculations reveal further coexistence regions where superconductivity is accompanied by incommensurate magnetic order. PMID:26991188
Possibility of superconductivity in the repulsive Hubbard model on the Shastry-Sutherland lattice
Kimura, Takashi; Kuroki, Kazuhiko; Arita, Ryotaro; Aoki, Hideo
2003-01-01
Possibility of superconductivity from electron repulsion in the Shastry-Sutherland lattice, which has a spin gap at half filling, is explored with the repulsive Hubbard model in the fluctuation-exchange approximation. We find that, while superconductivity is not favored around the half-filling, superconductivity is favored around the quarter-filling. Our results suggest that the Fermi surface nesting is more important than the spin dimerization for superconductivity.
Coexistence of incommensurate magnetism and superconductivity in the two-dimensional Hubbard model
Yamase, Hiroyuki; Eberlein, Andreas; Metzner, Walter
2015-01-01
We analyze the competition of magnetism and superconductivity in the two-dimensional Hubbard model with a moderate interaction strength, including the possibility of incommensurate spiral magnetic order. Using an unbiased renormalization group approach, we compute magnetic and superconducting order parameters in the ground state. In addition to previously established regions of Neel order coexisting with d-wave superconductivity, the calculations reveal further coexistence regions where super...
Four-point vertex in the Hubbard model and partial bosonization
Friederich, S.; Krahl, H. C.; Wetterich, C.
2010-01-01
Magnetic and superconducting instabilities in the two-dimensional t-t'-Hubbard model are discussed within a functional renormalization group approach. The fermionic four-point vertex is efficiently parametrized by means of partial bosonization. The exchange of composite bosons in the magnetic, charge density and superconducting channels accounts for the increase of the effective couplings with increasing length scale. We compute the pseudocritical temperature for the onset of local order in v...
Solving the Parquet Equations for the Hubbard Model beyond Weak Coupling
Tam, Ka-Ming; Fotso, H.; Yang, S. -X.; Lee, Tae-Woo; Moreno, J.; Ramanujam, J.; Jarrell, M.
2011-01-01
We find that imposing the crossing symmetry in the iteration process considerably extends the range of convergence for solutions of the parquet equations for the Hubbard model. When the crossing symmetry is not imposed, the convergence of both simple iteration and more complicated continuous loading (homotopy) methods are limited to high temperatures and weak interactions. We modify the algorithm to impose the crossing symmetry without increasing the computational complexity. We also imposed ...
Electronic properties of a generalized Hubbard model at half-filling
A generalized Hubbard model with correlated hoppings is studied at half-filling using exact diagonalization methods. For certain values of the hopping parameters our results for several static and dynamic correlation functions suggest the occurrence of a metal-insulator transition (MIT) at a finite value of the local Coulomb interaction UC. We identify the regions of the hopping parameters where the MIT is of the Mott type. In these regions, for large UC, we find a ferromagnetic ground state. (orig.)
On spectral properties of three-electron systems in the Hubbard model
We investigate spectral properties of a three-electron system in the framework of the Hubbard model. We prove that the essential spectrum of the system in a quartet state consists of a single segment and the three-electron bound state is absent. We show that the essential spectrum of the system in doublet states consists of unification of no more then three segments. We also prove that three-electron bound states exist in doublet states. (authors)
Bethe states for the two-site Bose-Hubbard model: a binomial approach
Santos, Gilberto; Foerster, Angela; Roditi, Itzhak
2015-01-01
We calculate explicitly the Bethe vectors states by the algebraic Bethe ansatz method with the $gl(2)$-invariant $R$-matrix for the two-site Bose-Hubbard model. Using a binomial expansion of the n-th power of a sum of two operators we get and solve a recursion equation. We calculate the scalar product and the norm of the Bethe vectors states. The form factors of the imbalance current operator are also computed.
The pairing correlations in the phased t-U Hubbard model
Liu Zi-Xin; Liu Ping; Liu Ya; Wen Sheng-Hui
2004-01-01
In this paper we have studied the phased t U Hubbard model. Using the constrained path Monte Carlo method,we investigated the effects of phase factor on pairing correlation functions in the ground state, and we found that the long-range correlations are dependent on the choice of phase factor, and for some special values of phase factor there exist long-range pairing correlations only in the strong coupling region.
Two-polariton bound states in the Jaynes-Cummings-Hubbard model
We examine the eigenstates of the one-dimensional Jaynes-Cummings-Hubbard model in the two-excitation subspace. We discover that two-excitation bound states emerge when the ratio of vacuum Rabi frequency to the tunneling rate between cavities exceeds a critical value. We determine the critical value as a function of the quasimomentum quantum number, and indicate that the bound states carry a strong correlation in which the two polaritons appear to be spatially confined together.
Anisotropic Hubbard model on a triangular lattice - spin dynamics in HoMnO3
Saptarshi Ghosh; Avinash Singh
2008-01-01
The recent neutron scattering data for spin-wave dispersion in HoMnO3 are well-described by an anisotropic Hubbard model on a triangular lattice with a planar (XY) spin anisotropy. Best fit indicates that magnetic excitations in HoMnO3 correspond to the strong-coupling limit / > ∼ 15, with planar exchange energy = 42/ ≃ 2.5 meV and planar anisotropy ≃ 0.35 meV.
Spin-state transition and phase separation in multi-orbital Hubbard model
Suzuki, Ryo; Watanabe, Tsutomu; Ishihara, Sumio
2009-01-01
We study spin-state transition and phase separation involving this transition based on the milti-orbital Hubbard model. Multiple spin states are realized by changing the energy separation between the two orbitals and the on-site Hund coupling. By utilizing the variational Monte-Carlo simulation, we analyze the electronic and magnetic structures in hole doped and undoped states. Electronic phase separation occurs between the low-spin band insulating state and the high-spin ferromagnetic metall...
Bosonization study of quantum phase transitions in the one-dimensional asymmetric Hubbard model
Wang, Z. G.; Chen, Y G; Gu, S. J.
2007-01-01
The quantum phase transitions in the one-dimensional asymmetric Hubbard model are investigated with the bosonization approach. The conditions for the phase transition from density wave to phase separation, the correlation functions and their exponents are obtained analytically. Our results show that the difference between the hopping integrals for up- and down-spin electrons is crucial for the happening of the phase separation. When the difference is large enough, the phase separation will ap...
Exact solution of the one-dimensional Hubbard model with arbitrary boundary magnetic fields
Li, Yuan-Yuan; Cao, Junpeng [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Yang, Wen-Li [Institute of Modern Physics, Northwest University, Xian 710069 (China); Beijing Center for Mathematics and Information Interdisciplinary Sciences, Beijing, 100048 (China); Shi, Kangjie [Institute of Modern Physics, Northwest University, Xian 710069 (China); Wang, Yupeng, E-mail: yupeng@iphy.ac.cn [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China)
2014-02-15
The one-dimensional Hubbard model with arbitrary boundary magnetic fields is solved exactly via the Bethe ansatz methods. With the coordinate Bethe ansatz in the charge sector, the second eigenvalue problem associated with the spin sector is constructed. It is shown that the second eigenvalue problem can be transformed into that of the inhomogeneous XXX spin chain with arbitrary boundary fields which can be solved via the off-diagonal Bethe ansatz method.
Lacki, M.; Delande, D; Zakrzewski, J.
2011-01-01
Using Fourier transform on a time series generated by unitary evolution, we extract many-body eigenstates of the Bose-Hubbard model corresponding to low energy excitations, which are generated when the insulator-superfluid phase transition is realized in a typical experiment. The analysis is conducted in a symmetric external potential both without and with and disorder. A simple classification of excitations in the absence disorder is provided. The evolution is performed assuming the presence...
Quantum Bose-Hubbard model with an evolving graph as a toy model for emergent spacetime
We present a toy model for interacting matter and geometry that explores quantum dynamics in a spin system as a precursor to a quantum theory of gravity. The model has no a priori geometric properties; instead, locality is inferred from the more fundamental notion of interaction between the matter degrees of freedom. The interaction terms are themselves quantum degrees of freedom so that the structure of interactions and hence the resulting local and causal structures are dynamical. The system is a Hubbard model where the graph of the interactions is a set of quantum evolving variables. We show entanglement between spatial and matter degrees of freedom. We study numerically the quantum system and analyze its entanglement dynamics. We analyze the asymptotic behavior of the classical model. Finally, we discuss analogues of trapped surfaces and gravitational attraction in this simple model.
Moment approach for the attractive Hubbard model in two dimensions: superconductivity
Full text. Using the moment of Nolting (Z. Phys. 225, 25 (1972) for the attractive Hubbard model in the superconducting phase, we have derived a set of three non-linear equations, the electron density, the superconducting order parameter, and the narrowing factor. Our starting point is the Ansatz that the diagonal spectral density is composed of three peaks while the off-diagonal spectral functional is composed of two. The third band, or upper Hubbard band, strongly renormalizes the other two, making the energy gap K dependent while the order parameter is pure s-wave. Our approach recuperates the BCS limit, weak coupling (U/t <<1) in a natural way. We solve these non-linear equations in a self-consistent way for intermediate coupling for U/t ∼ -4.0. Here we report the order parameter as function of temperature and compare it with the BCS result. (author)
SU(2) symmetry in a Hubbard model with spin-orbit coupling
ZHANG XiZheng; JIN Liang; SONG Zhi
2014-01-01
We study the underlying symmetry in a spin-orbit coupled tight-binding model with Hubbard interaction.It is shown that,in the absence of the on-site interaction,the system possesses the SU(2) symmetry arising from the time reversal symmetry.The influence of the on-site interaction on the symmetry depends on the topology of the networks:The SU(2) symmetry is shown to be the spin rotation symmetry of a simply-connected lattice even in the presence of the Hubbard interaction.On the contrary,the on-site interaction breaks the SU(2) symmetry of a multi-connected lattice.This fact indicates that a discrete spin-orbit coupled system has exclusive features from its counterpart in a continuous system.The obtained rigorous result is illustrated by a simple ring system.
Moskvin, A. S., E-mail: alexander.moskvin@urfu.ru [Ural Federal University (Russian Federation)
2015-09-15
We discuss the most prominent and intensively studied S = 1 pseudospin formalism for the extended bosonic Hubbard model (EBHM) with the on-site Hilbert space truncated to the three lowest occupation states n = 0, 1, 2. The EBHM Hamiltonian is a paradigmatic model for the highly topical field of ultracold gases in optical lattices. The generalized non-Heisenberg effective pseudospin Hamiltonian does provide a deep link with a boson system and a physically clear description of “the myriad of phases,” from uniform Mott insulating phases and density waves to two types of superfluids and supersolids. We argue that the 2D pseudospin system is prone to a topological phase separation and focus on several types of unconventional skyrmion-like topological structures in 2D boson systems, which have not been analyzed until now. The structures are characterized by a complicated interplay of insulating and two superfluid phases with a single- boson and two-boson condensation, respectively.
Ferromagnetism in the Hubbard model on a lattice of three coupled chains
We study the Hubbard model which is reduced to Mielke's flat-band model on the line graph of the two-leg ladder in a special case. In the flat-band case, the model exhibits saturated ferromagnetism when the electron number corresponds to ((1)/(6)) -filling+1. We show that, even in the non-flat-band case, the model with that number of electrons exhibits ferromagnetism when the on-site interaction is large, and that this is true for ((1)/(6)) -filling. We also give numerical evidence that the model with the nearly flat-band exhibits ferromagnetism for less than ((1)/(6)) -filling
Technical Review of the UNET2D Hydraulic Model
Perkins, William A. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Richmond, Marshall C. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
2009-05-18
The Kansas City District of the US Army Corps of Engineers is engaged in a broad range of river management projects that require knowledge of spatially-varied hydraulic conditions such as velocities and water surface elevations. This information is needed to design new structures, improve existing operations, and assess aquatic habitat. Two-dimensional (2D) depth-averaged numerical hydraulic models are a common tool that can be used to provide velocity and depth information. Kansas City District is currently using a specific 2D model, UNET2D, that has been developed to meet the needs of their river engineering applications. This report documents a tech- nical review of UNET2D.
QSAR Models for P-450 (2D6) Substrate Activity
Ringsted, Tine; Nikolov, Nikolai Georgiev; Jensen, Gunde Egeskov;
2009-01-01
activity relationship (QSAR) modelling systems. They cross validated (leave-groups-out) with concordances of 71%, 81% and 82%, respectively. Discrete organic European Inventory of Existing Commercial Chemical Substances (EINECS) chemicals were screened to predict an approximate percentage of CYP 2D6...... substrates. These chemicals are potentially present in the environment. The biological importance of the CYP 2D6 and the use of the software mentioned above were discussed....
Numerical studies of superconductivity in the two-dimensional Hubbard model
The question of superconductivity in the two-dimensional Hubbard model is reviewed. Emphasis is placed on the large-U limit of the single-band model and the relevance of this model to high-temperature superconductivity is discussed. Variational Monte Carlo work has shown that a nominally superconducting Gutzwiller or RVB state has essentially the same energy as the antiferromagnetic state for the half-filled (spin only) case. This state becomes a true d-wave superconductor for the less-than-half-filled (doped) case. This is an interference effect in which the phasing of the Cooper pairs acts to enhance antiferromagnetic spin correlations
Stability of ferromagnetism in Hubbard models with degenerate single-particle ground states
A Hubbard model with a Nd-fold degenerate single-particle ground state has ferromagnetic ground states if the number of electrons is less than or equal to Nd. It is shown rigorously that the local stability of ferromagnetism in such a model implies global stability: the model has only ferromagnetic ground states, if there are no single spin-flip ground states. If the number of electrons is equal to Nd , it is well known that the ferromagnetic ground state is unique if and only if the single-particle density matrix is irreducible. We present a simplified proof for this result. (author)
Numerical investigation of the 3D Hubbard model on a Linux cluster
We investigate numerically the magnetic properties of the 3D Isotropic and Anisotropic Hubbard model at half-filling on a Linux cluster. The behavior of the transition temperature as a function of the anisotropic hopping parameter is qualitatively described. In the Isotropic model we measure the scaling properties of the susceptibility finding agreement with the magnetic critical exponents of the 3D Heisenberg model. We describe several particularities concerning the implementation of our simulation in a cluster of personal computers paying special attention to the issues related with the parallelization of the algorithm
Local moment approach as a quantum impurity solver for the Hubbard model
Barman, Himadri
2016-07-01
The local moment approach (LMA) has presented itself as a powerful semianalytical quantum impurity solver (QIS) in the context of the dynamical mean-field theory (DMFT) for the periodic Anderson model and it correctly captures the low-energy Kondo scale for the single impurity model, having excellent agreement with the Bethe ansatz and numerical renormalization group (NRG) results. However, the most common correlated lattice model, the Hubbard model, has not been explored well within the LMA+DMFT framework beyond the insulating phase. Here in our work, within the framework we complete the filling-interaction phase diagram of the single band Hubbard model at zero temperature. Our formalism is generic to any particle filling and can be extended to finite temperature. We contrast our results with another QIS, namely the iterated perturbation theory (IPT) and show that the second spectral moment sum rule improves better as the Hubbard interaction strength grows stronger in LMA, whereas it severely breaks down after the Mott transition in IPT. For the metallic case, the Fermi liquid (FL) scaling agreement with the NRG spectral density supports the fact that the FL scale emerges from the inherent Kondo physics of the impurity model. We also show that, in the metallic phase, the FL scaling of the spectral density leads to universality which extends to infinite frequency range at infinite correlation strength (strong coupling). At large interaction strength, the off half-filling spectral density forms a pseudogap near the Fermi level and filling-controlled Mott transition occurs as one approaches the half-filling. As a response property, we finally study the zero temperature optical conductivity and find universal features such as absorption peak position governed by the FL scale and a doping independent crossing point, often dubbed the isosbestic point in experiments.
A VARIATIONAL MODEL FOR 2-D MICROPOLAR BLOOD FLOW
He Ji-huan
2003-01-01
The micropolar fluid model is an essential generalization of the well-established Navier-Stokes model in the sense that it takes into account the microstructure of the fluid.This paper is devolted to establishing a variational principle for 2-D incompressible micropolar blood flow.
Spin and charge dynamics in a one-dimensional two-band Hubbard model
A CuO chain with one or two holes doped is studied via the two-band Hubbard model in the large-U limit on a finite cluster. The quasiparticle band is Ek∼0.87J cos(2ka) with the bottom at ka=π/2. The quasiparticles are kinks which have the character of three-spin polarons. The copper spin excitations are incommensurate spin waves. The two doped holes repel each other very slightly, in contrast to the slight attraction in the t-J model. Spin-charge separation also occurs
SDW antiferromagnetic phase in the two-dimensional Hubbard model: Eliashberg approach
Szczes' niak, R. [Institute of Physics, Czestochowa University of Technology, Al. Armii Krajowej 19, 42-200 Czestochowa (Poland)], E-mail: szczesni@mim.pcz.czest.pl
2009-01-19
The two-dimensional Hubbard model was used for the description of the spin density wave (SDW) antiferromagnetic phase. The calculations were conducted in the framework of the Eliashberg formalism. The SDW phase that characterizes with the order parameter of the s-, extended s- or d-wave symmetry has been considered. The Eliashberg equations for the half-filled electron band have been constructed, with a use of which, it has been shown that only the SDW phase of the s-wave symmetry induces in the system. Next, the dependence of the s-wave SDW transition temperature on the value of the on-site Coulomb repulsion parameter was determined.
Eliashberg equations with momentum-dependent kernals for the two-dimensional Hubbard model
Mierzejewski, M.; Zielinski, J.; Entel, P. [Gerhard-Mercator-Univeitat, Duisburg (Germany)
1996-02-01
The authors discuss the impact of the strong electron phonon interactions on the physical properties of correlated electrons in the two-dimensional Hubbard model. An easy access to the physical properties of the superconducting state is obtained by solving the Eliashberg equations with explicit momentum-dependent kernels. In order to facilitate the numerical procedure to solve these equations, correlations are treated within the Gutzwiller approximation (i.e., mean-field-slave boson approximation). The authors results strongly support the view that d-wave symmetry is the most important feature of the superconducting state in the copper oxides. A possible extension beyond the mean field approximation is also presented.
The Mott metal-insulator transition in half-filled two-dimensional Hubbard models
Peyman Sahebsara
2008-06-01
Full Text Available We study the Mott transition in the two dimensional Hubbard model by using the variational cluster approximation. The transition potential obtained is roughly Uc ≈ 2 and 6 for square and triangular lattices, respectively. A comparison between results of this approximation and other quantum cluster methods is presented. Our zero-temperature calculation at strong coupling show that the transition on the triangular and square lattices occur at lower values of compared with other numerical techniques such as DMFT, CDMFT, and DCA. We also study the thermodynamic limit by an extrapolation to infinite size.
Metal-Insulator Transition in the Hubbard Model: Correlations and Spiral Magnetic Structures
Timirgazin, Marat A.; Igoshev, Petr A.; Arzhnikov, Anatoly K.; Irkhin, Valentin Yu.
2016-03-01
The metal-insulator transition (MIT) for the square, simple cubic, and body-centered cubic lattices is investigated within the t-t^' Hubbard model at half-filling by using both the generalized for the case of spiral order Hartree-Fock approximation (HFA) and Kotliar-Ruckenstein slave-boson approach. It turns out that the magnetic scenario of MIT becomes superior over the non-magnetic one. The electron correlations lead to some suppression of the spiral phases in comparison with HFA. We found the presence of a metallic antiferromagnetic (spiral) phase in the case of three-dimensional lattices.
Pressure dependence of a charge-transfer gap and a three-band Hubbard model
The three-band Hubbard Hamiltonian with an attractive oxygen-oxygen interaction Upp is investigated using the Hartree-Fock approximation. Such a Hamiltonian is assumed to be a generic model for CuO2 planes of high-Tc superconductors. Both superconducting and antiferromagnetic phases are found in the separate regions of the numerically obtained (Upp,δ) phase diagrams, where δ is the hole doping. It is found that the region of stability of the superconducting phase is enhanced with decreasing values of the charge-transfer gap, in good qualitative agreement with the experimental findings
Quantum phases of the Bose-Hubbard model in optical superlattices
We analyze the quantum phases of multicomponent Bose-Hubbard models in optical superlattices based on a mean-field method, that is, the decoupling approximation. The global phase diagrams exhibit complex patterns with various charge-density-wave orders for both one- and two-component cases. We further calculate the effective spin excitations for the two-component case in the strong-coupling region at unit filling, and show the existence of a spin-density-wave order. The results of our study can be tested straightforwardly with current cold-atom experimental techniques.
Superfluid-Mott-insulator transition in the spin-orbit-coupled Bose-Hubbard model
Işkın, Menderes; Bölükbaşı, Ahmet Tuna
2014-01-01
PHYSICAL REVIEW A 89, 043603 (2014) Superfluid–Mott-insulator transition in the spin-orbit-coupled Bose-Hubbard model A. T. Bolukbasi and M. Iskin Department of Physics, Koc¸ University, Rumelifeneri Yolu, 34450 Sariyer, Istanbul, Turkey (Received 3 January 2014; published 4 April 2014) We consider a square optical lattice in two dimensions and study the effects of both the strength and symmetry of spin-orbit coupling and Zeeman field on the ground-state, i.e.,Mott-insulator...
Mishra, A. K.; Kishore, R.
2016-08-01
We have obtained the exact expressions for the thermoelectric power and the Lorenz number for the infinite U Hubbard model using orthofermion approach. It is found that in one dimension, our results coincide with that of known exact results. In limiting cases, our exact expressions reduce to the known exact results at low and high temperature limits. We present our calculations for one and two dimensions for square as well as triangular lattices. A comparison between the thermoelectric power and Lorenz number for a free Fermi gas and noninteracting orthofermions has also been provided.
Supersolid and solitonic phases in the one-dimensional extended Bose-Hubbard model
We report our findings on the quantum phase transitions in cold bosonic atoms in a one-dimensional optical lattice using the finite-size density-matrix renormalization-group method in the framework of the extended Bose-Hubbard model. We consider wide ranges of values for the filling factors and the nearest-neighbor interactions. At commensurate fillings, we obtain two different types of charge-density wave phases and a Mott insulator phase. However, departure from commensurate fillings yields the exotic supersolid phase where both the crystalline and the superfluid orders coexist. In addition, we obtain the signatures for the solitary waves and the superfluid phase.
DEVELOPMENT OF 2D HUMAN BODY MODELING USING THINNING ALGORITHM
K. Srinivasan
2010-11-01
Full Text Available Monitoring the behavior and activities of people in Video surveillance has gained more applications in Computer vision. This paper proposes a new approach to model the human body in 2D view for the activity analysis using Thinning algorithm. The first step of this work is Background subtraction which is achieved by the frame differencing algorithm. Thinning algorithm has been used to find the skeleton of the human body. After thinning, the thirteen feature points like terminating points, intersecting points, shoulder, elbow, and knee points have been extracted. Here, this research work attempts to represent the body model in three different ways such as Stick figure model, Patch model and Rectangle body model. The activities of humans have been analyzed with the help of 2D model for the pre-defined poses from the monocular video data. Finally, the time consumption and efficiency of our proposed algorithm have been evaluated.
Lattice simulation of 2d Gross-Neveu-type models
Full text: We discuss a Monte Carlo simulation of 2d Gross-Neveu-type models on the lattice. The four-Fermi interaction is written as a Gaussian integral with an auxiliary field and the fermion determinant is included by reweighting. We present results for bulk quantities and correlators and compare them to a simulation using a fermion-loop representation. (author)
For systems of interacting, ultracold spin-zero neutral bosonic atoms, harmonically trapped and subject to an optical lattice potential, we derive an Extended Bose Hubbard (EBH) model by developing a systematic expansion for the Hamiltonian of the system in powers of the lattice parameters and of a scale parameter, the lattice attenuation factor. We identify the dominant terms that need to be retained in realistic experimental conditions, up to nearest-neighbor interactions and nearest-neighbor hoppings conditioned by the on-site occupation numbers. In the mean field approximation, we determine the free energy of the system and study the phase diagram both at zero and at finite temperature. At variance with the standard on site Bose Hubbard model, the zero-temperature phase diagram of the EBH model possesses a dual structure in the Mott insulating regime. Namely, for specific ranges of the lattice parameters, a density wave phase characterizes the system at integer fillings, with domains of alternating mean occupation numbers that are the atomic counterparts of the domains of staggered magnetizations in an antiferromagnetic phase. We show as well that in the EBH model, a zero-temperature quantum phase transition to pair superfluidity is, in principle, possible, but completely suppressed at the lowest order in the lattice attenuation factor. Finally, we determine the possible occurrence of the different phases as a function of the experimentally controllable lattice parameters
The cell representation of the three-band Hubbard model
Moskalenko, V A; Marinaro, M; Digor, D F; Grecu, D
2002-01-01
The d-p model is reformulated in the representation of the Wannier orthogonalized copper and oxygen orbitals. The exact account of the holes hybridization on the oxygen ions is accomplished in this work in contrast to the other ones. Two diagonalized fermion cells of the oxygen holes mode are used for this purpose alongside with the copper holes mode. These diagonalized modes are characterized by essentially different local energies, that noticeably affects the theory results. The noncommutation of the oxygen Hamiltonian diagonalization operation and the Wannier orbitals orthogonalization by the copper lattice nodes is noted. The cell orbital of the oxygen holes, related to the CuO sub 4 ion complex, proves to be the superposition of these two diagonalized orbitals on our approach. The obtained Hamiltonian constitutes the components sum, the members whereof have the different number of the copper lattice nodes indices. The local component is the high set one. All main states of the cluster representation are ...
Spectral function of the ionic Hubbard model (IHM)
Bulut, Sinan; Atkinson, Bill
2010-03-01
Using two-pole approximations, which are based on the equation of motion method, we calculate the excitation spectrum of the one dimensional IHM. To be specific, we use the composite operator method and the Roth-approximation. Though very simple in nature, these approximations capture the physics of the IHM qualitatively at least. As is predicted by several other numerical and/or theoretical studies, a bond-order (BO) phase is given by these approximate methods. In the BO phase, atoms in the system are dimerized leading to a gap in the excitation spectrum. We find that the BO phase flattens both low and high-energy bands. When the BO phase is suppressed, however, the system can be driven from the band-insulating phase to the metal one by electron-electron repulsions, which is somewhat counter-intuitive. Additionally, two-pole approximations generate a reasonably good DOS spectrum of this model when compared with exact numerical results for small systems.
2D Models for Dust-driven AGB Star Winds
Woitke, P
2006-01-01
New axisymmetric (2D) models for dust-driven winds of C-stars are presented which include hydrodynamics with radiation pressure on dust, equilibrium chemistry and time-dependent dust formation with coupled grey Monte Carlo radiative transfer. Considering the most simple case without stellar pulsation (hydrostatic inner boundary condition) these models reveal a more complex picture of the dust formation and wind acceleration as compared to earlier published spherically symmetric (1D) models. The so-called exterior $\\kappa$-mechanism causes radial oscillations with short phases of active dust formation between longer phases without appreciable dust formation, just like in the 1D models. However, in 2D geometry, the oscillations can be out-of-phase at different places above the stellar atmosphere which result in the formation of dust arcs or smaller caps that only occupy a certain fraction of the total solid angle. These dust structures are accelerated outward by radiation pressure, expanding radially and tangen...
Mott-insulator-to-superfluid transition in the Bose-Hubbard model: A strong-coupling approach
We present a strong-coupling expansion of the Bose-Hubbard model which describes both the superfluid and the Mott phases of ultracold bosonic atoms in an optical lattice. By performing two successive Hubbard-Stratonovich transformations of the intersite hopping term, we derive an effective action which provides a suitable starting point to study the strong-coupling limit of the Bose-Hubbard model. This action can be analyzed by taking into account Gaussian fluctuations about the mean-field approximation as in the Bogoliubov theory of the weakly interacting Bose gas. In the Mott phase, we reproduce results of previous mean-field theories and also calculate the momentum distribution function. In the superfluid phase, we find a gapless spectrum and compare our results with the Bogoliubov theory
Johnson, T. H.; Yuan, Y.; Bao, W.; Clark, S. R.; Foot, C.; Jaksch, D.
2016-06-01
We investigate cold bosonic impurity atoms trapped in a vortex lattice formed by condensed bosons of another species. We describe the dynamics of the impurities by a bosonic Hubbard model containing occupation-dependent parameters to capture the effects of strong impurity-impurity interactions. These include both a repulsive direct interaction and an attractive effective interaction mediated by the Bose-Einstein condensate. The occupation dependence of these two competing interactions drastically affects the Hubbard model phase diagram, including causing the disappearance of some Mott lobes.
Johnson, T H; Yuan, Y; Bao, W; Clark, S R; Foot, C; Jaksch, D
2016-06-17
We investigate cold bosonic impurity atoms trapped in a vortex lattice formed by condensed bosons of another species. We describe the dynamics of the impurities by a bosonic Hubbard model containing occupation-dependent parameters to capture the effects of strong impurity-impurity interactions. These include both a repulsive direct interaction and an attractive effective interaction mediated by the Bose-Einstein condensate. The occupation dependence of these two competing interactions drastically affects the Hubbard model phase diagram, including causing the disappearance of some Mott lobes. PMID:27367366
Can the Hubbard model explain the steps observed in the magnetization curve of {Ni4Mo12}?
The low-temperature magnetization curve of the magnetic molecule {Ni4Mo12} features four nonequidistant steps which cannot be explained using a Heisenberg model. In his article, V. Kostyuchenko presents a spin-1 model with biquadratic and three-spin interactions and claims that it is the strong coupling limit of a certain Hubbard model. This spin-1 model correctly predicts the position of the steps in the magnetization curve. We investigate whether the Hubbard model proposed in is really capable of describing {Ni4Mo12}. To this end, we calculate its eigenvalues using numerical exact diagonalization and try to fit its parameters to the experimental magnetization data. We are unable to find suitable fit parameters although the parameter space of the model is only two-dimensional. Therefore, we analyze the strong coupling limit of the Hubbard model and rederive its effective spin model up to order O(U-3). The spin Hamiltonian which we obtain differs from the one presented by Kostyuchenko. We arrive at the final conclusion that the Hubbard model as proposed in is not suited to describe the molecule {Ni4Mo12}.
Mazumdar, S.; Clay, R. T.
2008-01-01
We demonstrate a robust frustration-driven charge-order to superconductivity transition in the half-filled negative-U extended Hubbard model. Superconductivity extends over a broad region of the parameter space. We argue that the model provides the correct insight to understanding unconventional superconductivity in the organic charge-transfer solids and other quarter-filled systems.
Modeling 2D and 3D Horizontal Wells Using CVFA
Chen, Zhangxin; Huan, Guanren; Li, Baoyan
2003-01-01
In this paper we present an application of the recently developed control volume function approximation (CVFA) method to the modeling and simulation of 2D and 3D horizontal wells in petroleum reservoirs. The base grid for this method is based on a Voronoi grid. One of the features of the CVFA is that the flux at the interfaces of control volumes can be accurately computed via function approximations. Also, it reduces grid orientation effects and applies to any shape of eleme...
Long-range orders and spin/orbital freezing in the two-band Hubbard model
Steiner, Karim; Hoshino, Shintaro; Nomura, Yusuke; Werner, Philipp
2016-08-01
We solve the orbitally degenerate two-band Hubbard model within dynamical mean field theory and map out the instabilities to various symmetry-broken phases based on an analysis of the corresponding lattice susceptibilities. Phase diagrams as a function of the Hund coupling parameter J are obtained both for the model with rotationally invariant interaction and for the model with Ising-type anisotropy. For negative J , an intraorbital spin-singlet superconducting phase appears at low temperatures, while the normal state properties are characterized by an orbital-freezing phenomenon. This is the negative-J analog of the recently discovered fluctuating-moment induced s -wave spin-triplet superconductivity in the spin-freezing regime of multiorbital models with J >0 .
A Quantum Mermin-Wagner Theorem for a Generalized Hubbard Model
Mark Kelbert
2013-01-01
Full Text Available This paper is the second in a series of papers considering symmetry properties of bosonic quantum systems over 2D graphs, with continuous spins, in the spirit of the Mermin-Wagner theorem. In the model considered here the phase space of a single spin is ℋ1=L2(M, where M is a d-dimensional unit torus M=ℝd/ℤd with a flat metric. The phase space of k spins is ℋk=L2sym(Mk, the subspace of L2(Mk formed by functions symmetric under the permutations of the arguments. The Fock space H=⊕k=0,1,…ℋk yields the phase space of a system of a varying (but finite number of particles. We associate a space H≃H(i with each vertex i∈Γ of a graph (Γ,ℰ satisfying a special bidimensionality property. (Physically, vertex i represents a heavy “atom” or “ion” that does not move but attracts a number of “light” particles. The kinetic energy part of the Hamiltonian includes (i -Δ/2, the minus a half of the Laplace operator on M, responsible for the motion of a particle while “trapped” by a given atom, and (ii an integral term describing possible “jumps” where a particle may join another atom. The potential part is an operator of multiplication by a function (the potential energy of a classical configuration which is a sum of (a one-body potentials U(1(x, x∈M, describing a field generated by a heavy atom, (b two-body potentials U(2(x,y, x,y∈M, showing the interaction between pairs of particles belonging to the same atom, and (c two-body potentials V(x,y, x,y∈M, scaled along the graph distance d(i,j between vertices i,j∈Γ, which gives the interaction between particles belonging to different atoms. The system under consideration can be considered as a generalized (bosonic Hubbard model. We assume that a connected Lie group G acts on M, represented by a Euclidean space or torus of dimension d'≤d, preserving the metric and the volume in M. Furthermore, we suppose that the potentials U(1, U(2, and V are G-invariant. The result
Quantum disordered insulating phase in the frustrated cubic-lattice Hubbard model
Laubach, Manuel; Joshi, Darshan G.; Reuther, Johannes; Thomale, Ronny; Vojta, Matthias; Rachel, Stephan
2016-01-01
In the quest for quantum spin liquids in three spatial dimensions (3D), we study the half-filled Hubbard model on the simple cubic lattice with hopping processes up to third neighbors. Employing the variational cluster approach (VCA), we determine the zero-temperature phase diagram: In addition to a paramagnetic metal at small interaction strength U and various antiferromagnetic insulators at large U , we find an intermediate-U antiferromagnetic metal. Most interestingly, we also identify a nonmagnetic insulating region, extending from intermediate to strong U . Using VCA results in the large-U limit, we establish the phase diagram of the corresponding J1-J2-J3 Heisenberg model. This is qualitatively confirmed—including the nonmagnetic region—using spin-wave theory. Further analysis reveals a striking similarity to the behavior of the J1-J2 square-lattice Heisenberg model, suggesting that the nonmagnetic region may host a 3D spin-liquid phase.
Exactly solvable models for 2D interacting fermions
I discuss many-body models for correlated fermions in two space dimensions which can be solved exactly using group theory. The simplest example is a model of a quantum Hall system: two-dimensional (2D) fermions in a constant magnetic field and a particular non-local four-point interaction. It is exactly solvable due to a dynamical symmetry corresponding to the Lie algebra gl∞ + gl∞. There is an algorithm to construct all energy eigenvalues and eigenfunctions of this model. The latter are, in general, many-body states with spatial correlations. The model also has a non-trivial zero temperature phase diagram. I point out that this QH model can be obtained from a more realistic one using a truncation procedure generalizing a similar one leading to mean field theory. Applying this truncation procedure to other 2D fermion models I obtain various simplified models of increasing complexity which generalize mean field theory by taking into account non-trivial correlations but nevertheless are treatable by exact methods
Magnetic properties of Hubbard-sigma model with three-dimensionality
It has been broadly accepted that the magnetism may play an important role in the high-Tc superconductivity in the lamellar CuO2 materials. In this paper, based on a Hubbard-inspired CP1 or S2 nonlinear σ model, we give a quantitative study of some magnetic properties in and around the Neel ordered state of three-dimensional quantum antiferromagnets such as La2CuO4 with and without small hole doping. Our model is a (3+1) dimensional effective field theory describing the low energy spin dynamics of a three-dimensional Hubbard model with a very weak interlayer coupling. The effect of hole dynamics is taken into account in the leading approximation by substituting the CP1 coupling and the spin-wave velocity with 'effective' ones determined by the concentration and the one-loop correction of hole fermions. Stationary-phase equations for the one-loop effective potential of S2 model are analyzed. Based on them, various magnetic properties of the system, such as the behavior of Neel temperature, spin correlation length, staggered magnetization, specific heat and susceptibility as functions of anisotropic parameter, temperature, etc. are investigated in detail. The results show that our anisotropic field theory model with certain values of parameters gives a good description of the magnetic properties in both the ordered and the disordered phases indicated by experiments on La2CuO4. The part of the above results is supported by the renormalization-group analysis. In the doped case it is observed that the existence of holes destroys the long-range order and their hopping effect is large. (author)
Thermodynamics of the Hubbard model on stacked honeycomb and square lattices
Imriška, Jakub; Gull, Emanuel; Troyer, Matthias
2016-07-01
We present a numerical study of the Hubbard model on simply stacked honeycomb and square lattices, motivated by a recent experimental realization of such models with ultracold atoms in optical lattices. We perform simulations with different interlayer coupling and interaction strengths and obtain Néel transition temperatures and entropies. We provide data for the equation of state to enable comparisons of experiments and theory. We find an enhancement of the short-range correlations in the anisotropic lattices compared to the isotropic cubic lattice, in parameter regimes suitable for the interaction driven adiabatic cooling. Supplementary material in the form of one zip file available from the Jounal web page at http://dx.doi.org/10.1140/epjb/e2016-70146-y
A Simple Hubbard Model for the Excited States of $\\pi$ Conjugated -acene Molecules
Sadeq, Z S
2015-01-01
In this paper we present a model that elucidates in a simple way the electronic excited states of $\\pi$ conjugated -acene molecules such as tetracene, pentacene, and hexacene. We use a tight-binding and truncated Hubbard model written in the electron-hole basis to describe the low lying excitations with reasonable quantitative accuracy. We are able to produce semi-analytic wavefunctions for the electronic states of the system, which allows us to compute the density correlation functions for various states such as the ground state, the first two singly excited states, and the lowest lying doubly excited state. We show that in this lowest lying doubly excited state, a state which has been speculated as to being involved in the singlet fission process, the electrons and holes behave in a triplet like manner.
Bilayer Hubbard model for 3He: a cluster dynamical mean-field calculation
Inspired by recent experiments on bilayer 3He, we consider a bilayer Hubbard model on a triangular lattice. For appropriate model parameters, we observe a band-selective Mott transition at a critical chemical potential, μc, corresponding to the solidification of the fermions in the first layer. The growth of the effective mass on the metallic side (μ c) is cut off by a first order transition in which the first layer fermions drop out of the Luttinger volume and their spin degrees of freedom become locked in a spin singlet state. These results are obtained from a cluster dynamical mean-field calculation on an eight-site cluster with a quantum Monte Carlo cluster solver.
Orientational bond and Néel order in the two-dimensional ionic Hubbard model
Hafez-Torbati, Mohsen; Uhrig, Götz S.
2016-05-01
Unconventional phases often occur where two competing mechanisms compensate. An excellent example is the ionic Hubbard model where the alternating local potential δ , favoring a band insulator (BI), competes with the local repulsion U , favoring a Mott insulator (MI). By continuous unitary transformations we derive effective models in which we study the softening of various excitons. The softening signals the instability towards new phases that we describe on the mean-field level. On increasing U from the BI in two dimensions, we find a bond-ordered phase breaking orientational symmetry due to a d -wave component. Then, antiferromagnetic order appears coexisting with the d -wave bond order. Finally, the d -wave order vanishes and a Néel-type MI persists.
Quantum phase transition of light in the Rabi–Hubbard model
We discuss the physics of the Rabi–Hubbard model describing large arrays of coupled cavities interacting with two level atoms via a Rabi nonlinearity. We show that the inclusion of counter-rotating terms in the light–matter interaction, often neglected in theoretical descriptions based on Jaynes–Cumming models, is crucial to stabilize finite-density quantum phases of correlated photons with no need for an artificially engineered chemical potential. We show that the physical properties of these phases and the quantum phase transition occurring between them is remarkably different from those of interacting bosonic massive quantum particles. The competition between photon delocalization and Rabi nonlinearity drives the system across a novel Z2 parity symmetry-breaking quantum phase transition between two gapped phases, a Rabi insulator and a delocalized super-radiant phase. (paper)
Panas, J.; Kauch, Anna; Kuneš, Jan; Vollhardt, D.; Byczuk, K.
2015-01-01
Roč. 92, č. 4 (2015), "045102-1"-"045102-9". ISSN 1098-0121 Institutional support: RVO:68378271 Keywords : Bose-Hubbard model * Bose-Einstein condensation * superfluidity Subject RIV: BE - Theoretical Physics Impact factor: 3.736, year: 2014
Zakrzewski, Jakub; Delande, Dominique
2007-01-01
The quantum phase transition point between the insulator and the superfluid phase at unit filling factor of the infinite one-dimensional Bose-Hubbard model is numerically computed with a high accuracy, better than current state of the art calculations. The method uses the infinite system version of the time evolving block decimation algorithm, here tested in a challenging case.
Gutzwiller wave function for finite systems: superconductivity in the Hubbard model.
Tomski, Andrzej; Kaczmarczyk, Jan
2016-05-01
We study the superconducting phase of the Hubbard model using the Gutzwiller variational wave function (GWF) and the recently proposed diagrammatic expansion technique (DE-GWF). The DE-GWF method works on the level of the full GWF and in the thermodynamic limit. Here, we consider a finite-size system to study the accuracy of the results as a function of the system size (which is practically unrestricted). We show that the finite-size scaling used, e.g. in the variational Monte Carlo method can lead to significant, uncontrolled errors. The presented research is the first step towards applying the DE-GWF method in studies of inhomogeneous situations, including systems with impurities, defects, inhomogeneous phases, or disorder. PMID:27023047
Quantum Monte Carlo simulations of the one-dimensional extended Hubbard model
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
Studies on entanglement entropy for Hubbard model with hole-doping and external magnetic field
By using the density matrix renormalization group (DMRG) method for the one-dimensional (1D) Hubbard model, we have studied the von Neumann entropy of a quantum system, which describes the entanglement of the system block and the rest of the chain. It is found that there is a close relation between the entanglement entropy and properties of the system. The hole-doping can alter the charge-charge and spin-spin interactions, resulting in charge polarization along the chain. By comparing the results before and after the doping, we find that doping favors increase of the von Neumann entropy and thus also favors the exchange of information along the chain. Furthermore, we calculated the spin and entropy distribution in external magnetic filed. It is confirmed that both the charge-charge and the spin-spin interactions affect the exchange of information along the chain, making the entanglement entropy redistribute
Critical points of the Bose–Hubbard model with three-body local interaction
Avila, C.A.; Franco, R. [Departamento de Física, Universidad Nacional de Colombia, A.A. 5997, Bogotá (Colombia); Souza, A.M.C. [Departamento de Física, Universidade Federal de Sergipe, 49100-000 São Cristovão, SE (Brazil); Figueira, M.S. [Instituto de Física, Universidade Federal Fluminense, Av. Litorânea s/n, 24210-346 Niterói, Rio de Janeiro (Brazil); Silva-Valencia, J., E-mail: jsilvav@unal.edu.co [Departamento de Física, Universidad Nacional de Colombia, A.A. 5997, Bogotá (Colombia)
2014-09-12
Using the density matrix renormalization group method, we study a one-dimensional system of bosons that interact with a local three-body term. We calculate the phase diagram for higher densities, where the Mott insulator lobes are surrounded by the superfluid phase. We also show that the Mott insulator lobes always grow as a function of the density. The critical points of the Kosterlitz–Thouless transitions were determined through the von Neumann block entropy, and its dependence on the density is given by a power law with a negative exponent. - Highlights: • We studied the Bose–Hubbard model with a local three-body interaction term. • We show that the Mott insulator lobes always grow as a function of the density. • We found a power law dependence of the critical point position with the density.
Critical points of the Bose–Hubbard model with three-body local interaction
Using the density matrix renormalization group method, we study a one-dimensional system of bosons that interact with a local three-body term. We calculate the phase diagram for higher densities, where the Mott insulator lobes are surrounded by the superfluid phase. We also show that the Mott insulator lobes always grow as a function of the density. The critical points of the Kosterlitz–Thouless transitions were determined through the von Neumann block entropy, and its dependence on the density is given by a power law with a negative exponent. - Highlights: • We studied the Bose–Hubbard model with a local three-body interaction term. • We show that the Mott insulator lobes always grow as a function of the density. • We found a power law dependence of the critical point position with the density
Magnetic phase diagram of the Hubbard model with next-nearest-neighbour hopping
We calculate the magnetic phase diagram of the Hubbard model for a Bethe lattice with nearest-neighbour (NN) hopping t1 and next-nearest-neighbour (NNN) hopping t2 in the limit of infinite coordination. We use the amplitude t2/t1 of the NNN hopping to tune the density of states (DOS) of the non-interacting system from a situation with particle-hole symmetry to an asymmetric one with van-Hove singularities at the lower (t2/t1>0) respectively upper (t2/t12/t1|. For this strongly asymmetric situation, we find rather extended parameter regions with ferromagnetic states and regions with antiferromagnetic states.
Algebraic geometry methods associated to the one-dimensional Hubbard model
Martins, M. J.
2016-06-01
In this paper we study the covering vertex model of the one-dimensional Hubbard Hamiltonian constructed by Shastry in the realm of algebraic geometry. We show that the Lax operator sits in a genus one curve which is not isomorphic but only isogenous to the curve suitable for the AdS/CFT context. We provide an uniformization of the Lax operator in terms of ratios of theta functions allowing us to establish relativistic like properties such as crossing and unitarity. We show that the respective R-matrix weights lie on an Abelian surface being birational to the product of two elliptic curves with distinct J-invariants. One of the curves is isomorphic to that of the Lax operator but the other is solely fourfold isogenous. These results clarify the reason the R-matrix can not be written using only difference of spectral parameters of the Lax operator.
Effect of interactions, disorder and magnetic field in the Hubbard model in two dimensions
N Trivedi; P J H Denteneer; D Heidarian; R T Scaletar
2005-06-01
The effects of both interactions and Zeeman magnetic field in disordered electronic systems are explored in the Hubbard model on a square lattice. We investigate the thermodynamic (density, magnetization, density of states) and transport (conductivity) properties using determinantal quantum Monte Carlo and inhomogeneous Hartree Fock techniques. We find that at half filling there is a novel metallic phase at intermediate disorder that is sandwiched between a Mott insulator and an Anderson insulator. The metallic phase is highly inhomogeneous and coexists with antiferromagnetic long-range order. At quarter filling also the combined effects of disorder and interactions produce a conducting state which can be destroyed by applying a Zeeman field, resulting in a magnetic field-driven transition. We discuss the implication of our results for experiments.
Gutzwiller wave function for finite systems: superconductivity in the Hubbard model
Tomski, Andrzej; Kaczmarczyk, Jan
2016-05-01
We study the superconducting phase of the Hubbard model using the Gutzwiller variational wave function (GWF) and the recently proposed diagrammatic expansion technique (DE-GWF). The DE-GWF method works on the level of the full GWF and in the thermodynamic limit. Here, we consider a finite-size system to study the accuracy of the results as a function of the system size (which is practically unrestricted). We show that the finite-size scaling used, e.g. in the variational Monte Carlo method can lead to significant, uncontrolled errors. The presented research is the first step towards applying the DE-GWF method in studies of inhomogeneous situations, including systems with impurities, defects, inhomogeneous phases, or disorder.
2D numerical modelling of meandering channel formation
XIAO, Y.; ZHOU, G.; YANG, F. S.
2016-03-01
A 2D depth-averaged model for hydrodynamic sediment transport and river morphological adjustment was established. The sediment transport submodel takes into account the influence of non-uniform sediment with bed surface armoring and considers the impact of secondary flow in the direction of bed-load transport and transverse slope of the river bed. The bank erosion submodel incorporates a simple simulation method for updating bank geometry during either degradational or aggradational bed evolution. Comparison of the results obtained by the extended model with experimental and field data, and numerical predictions validate that the proposed model can simulate grain sorting in river bends and duplicate the characteristics of meandering river and its development. The results illustrate that by using its control factors, the improved numerical model can be applied to simulate channel evolution under different scenarios and improve understanding of patterning processes.
2D numerical modelling of meandering channel formation
Y Xiao; G Zhou; F S Yang
2016-03-01
A 2D depth-averaged model for hydrodynamic sediment transport and river morphological adjustment was established. The sediment transport submodel takes into account the influence of non-uniform sediment with bed surface armoring and considers the impact of secondary flow in the direction of bed-loadtransport and transverse slope of the river bed. The bank erosion submodel incorporates a simple simulation method for updating bank geometry during either degradational or aggradational bed evolution. Comparison of the results obtained by the extended model with experimental and field data, and numericalpredictions validate that the proposed model can simulate grain sorting in river bends and duplicate the characteristics of meandering river and its development. The results illustrate that by using its control factors, the improved numerical model can be applied to simulate channel evolution under differentscenarios and improve understanding of patterning processes.
Brane Brick Models and 2d (0,2) Triality
Franco, Sebastian; Seong, Rak-Kyeong
2016-01-01
We provide a brane realization of 2d (0,2) Gadde-Gukov-Putrov triality in terms of brane brick models. These are Type IIA brane configurations that are T-dual to D1-branes over singular toric Calabi-Yau 4-folds. Triality translates into a local transformation of brane brick models, whose simplest representative is a cube move. We present explicit examples and construct their triality networks. We also argue that the classical mesonic moduli space of brane brick model theories, which corresponds to the probed Calabi-Yau 4-fold, is invariant under triality. Finally, we discuss triality in terms of phase boundaries, which play a central role in connecting Calabi-Yau 4-folds to brane brick models.
2-D Composite Model for Numerical Simulations of Nonlinear Waves
2000-01-01
－ A composite model, which is the combination of Boussinesq equations and Volume of Fluid (VOF) method, has been developed for 2-D time-domain computations of nonlinear waves in a large region. The whole computational region Ω is divided into two subregions. In the near-field around a structure, Ω2, the flow is governed by 2-D Reynolds Averaged Navier-Stokes equations with a turbulence closure model of k-ε equations and numerically solved by the improved VOF method; whereas in the subregion Ω1 (Ω1 = Ω - Ω2) the flow is governed by one-D Boussinesq equations and numerically solved with the predictor-corrector algorithm. The velocity and the wave surface elevation are matched on the common boundary of the two subregions. Numerical tests have been conducted for the case of wave propagation and interaction with a wave barrier. It is shown that the composite model can help perform efficient computation of nonlinear waves in a large region with the complicated flow fields near structures taken into account.
Statistical mechanics of shell models for 2D-Turbulence
Aurell, E; Crisanti, A; Frick, P; Paladin, G; Vulpiani, A
1994-01-01
We study shell models that conserve the analogues of energy and enstrophy, hence designed to mimic fluid turbulence in 2D. The main result is that the observed state is well described as a formal statistical equilibrium, closely analogous to the approach to two-dimensional ideal hydrodynamics of Onsager, Hopf and Lee. In the presence of forcing and dissipation we observe a forward flux of enstrophy and a backward flux of energy. These fluxes can be understood as mean diffusive drifts from a source to two sinks in a system which is close to local equilibrium with Lagrange multipliers (``shell temperatures'') changing slowly with scale. The dimensional predictions on the power spectra from a supposed forward cascade of enstrophy, and from one branch of the formal statistical equilibrium, coincide in these shell models at difference to the corresponding predictions for the Navier-Stokes and Euler equations in 2D. This coincidence have previously led to the mistaken conclusion that shell models exhibit a forward ...
Finite state models of constrained 2d data
Justesen, Jørn
2004-01-01
This paper considers a class of discrete finite alphabet 2D fields that can be characterized using tools front finite state machines and Markov chains. These fields have several properties that greatly simplify the analysis of 2D coding methods.......This paper considers a class of discrete finite alphabet 2D fields that can be characterized using tools front finite state machines and Markov chains. These fields have several properties that greatly simplify the analysis of 2D coding methods....
A 2D channel-clogging biofilm model.
Winstanley, H F; Chapwanya, M; Fowler, A C; O'Brien, S B G
2015-09-01
We present a model of biofilm growth in a long channel where the biomass is assumed to have the rheology of a viscous polymer solution. We examine the competition between growth and erosion-like surface detachment due to the flow. A particular focus of our investigation is the effect of the biofilm growth on the fluid flow in the pores, and the issue of whether biomass can grow sufficiently to shut off fluid flow through the pores, thus clogging the pore space. Net biofilm growth is coupled along the pore length via flow rate and nutrient transport in the pore flow. Our 2D model extends existing results on stability of 1D steady state biofilm thicknesses to show that, in the case of flows driven by a fixed pressure drop, full clogging of the pore can indeed happen in certain cases dependent on the functional form of the detachment term. PMID:25240390
On the particle-hole symmetry of the fermionic spinless Hubbard model in D=1
M.T. Thomaz
2014-06-01
Full Text Available We revisit the particle-hole symmetry of the one-dimensional (D=1 fermionic spinless Hubbard model, associating that symmetry to the invariance of the Helmholtz free energy of the one-dimensional spin-1/2 XXZ Heisenberg model, under reversal of the longitudinal magnetic field and at any finite temperature. Upon comparing two regimes of that chain model so that the number of particles in one regime equals the number of holes in the other, one finds that, in general, their thermodynamics is similar, but not identical: both models share the specific heat and entropy functions, but not the internal energy per site, the first-neighbor correlation functions, and the number of particles per site. Due to that symmetry, the difference between the first-neighbor correlation functions is proportional to the z-component of magnetization of the XXZ Heisenberg model. The results presented in this paper are valid for any value of the interaction strength parameter V, which describes the attractive/null/repulsive interaction of neighboring fermions.
Maximizing entropy of image models for 2-D constrained coding
Forchhammer, Søren; Danieli, Matteo; Burini, Nino;
2010-01-01
This paper considers estimating and maximizing the entropy of two-dimensional (2-D) fields with application to 2-D constrained coding. We consider Markov random fields (MRF), which have a non-causal description, and the special case of Pickard random fields (PRF). The PRF are 2-D causal finite...... of the Markov random field defined by the 2-D constraint is estimated to be (upper bounded by) 0.8570 bits/symbol using the iterative technique of Belief Propagation on 2 £ 2 finite lattices. Based on combinatorial bounding techniques the maximum entropy for the constraint was determined to be 0.848....
Cascading rainfall uncertainties into 2D inundation impact models
Souvignet, Maxime; de Almeida, Gustavo; Champion, Adrian; Garcia Pintado, Javier; Neal, Jeff; Freer, Jim; Cloke, Hannah; Odoni, Nick; Coxon, Gemma; Bates, Paul; Mason, David
2013-04-01
Existing precipitation products show differences in their spatial and temporal distribution and several studies have presented how these differences influence the ability to predict hydrological responses. However, an atmospheric-hydrologic-hydraulic uncertainty cascade is seldom explored and how, importantly, input uncertainties propagate through this cascade is still poorly understood. Such a project requires a combination of modelling capabilities, runoff generation predictions based on those rainfall forecasts, and hydraulic flood wave propagation based on the runoff predictions. Accounting for uncertainty in each component is important in decision making for issuing flood warnings, monitoring or planning. We suggest a better understanding of uncertainties in inundation impact modelling must consider these differences in rainfall products. This will improve our understanding of the input uncertainties on our predictive capability. In this paper, we propose to address this issue by i) exploring the effects of errors in rainfall on inundation predictive capacity within an uncertainty framework, i.e. testing inundation uncertainty against different comparable meteorological conditions (i.e. using different rainfall products). Our method cascades rainfall uncertainties into a lumped hydrologic model (FUSE) within the GLUE uncertainty framework. The resultant prediction uncertainties in discharge provide uncertain boundary conditions, which are cascaded into a simplified shallow water 2D hydraulic model (LISFLOOD-FP). Rainfall data captured by three different measurement techniques - rain gauges, gridded data and numerical weather predictions (NWP) models are used to assess the combined input data and model parameter uncertainty. The study is performed in the Severn catchment over the period between June and July 2007, where a series of rainfall events causing record floods in the study area). Changes in flood area extent are compared and the uncertainty envelope is
Multiplons in the two-hole excitation spectra of the one-dimensional Hubbard model
Rausch, Roman; Potthoff, Michael
2016-02-01
Using the density-matrix renormalization group in combination with the Chebyshev polynomial expansion technique, we study the two-hole excitation spectrum of the one-dimensional Hubbard model in the entire filling range from the completely occupied band (n = 2) down to half-filling (n = 1). For strong interactions, the spectra reveal multiplon physics, i.e., relevant final states are characterized by two (doublon), three (triplon), four (quadruplon) and more holes, potentially forming stable compound objects or resonances with finite lifetime. These give rise to several satellites in the spectra with largely different spectral weights as well as to different two-hole, doublon-hole, two-doublon etc continua. The complex multiplon phenomenology is analyzed by interpreting not only local and k-resolved two-hole spectra but also three- and four-hole spectra for the Hubbard model and by referring to effective low-energy models. In addition, a filter-operator technique is presented and applied which allows to extract specific information on the final states at a given excitation energy. While multiplons composed of an odd number of holes do neither form stable compounds nor well-defined resonances unless a nearest-neighbor density interaction V is added to the Hamiltonian, the doublon and the quadruplon are well-defined resonances. The k-resolved four-hole spectrum at n = 2 represents an interesting special case where a completely stable quadruplon turns into a resonance by merging with the doublon-doublon continuum at a critical wave vector. For all fillings with n\\gt 1, the doublon lifetime is strongly k-dependent and is even infinite at the Brillouin zone edges as demonstrated by k-resolved two-hole spectra. This can be traced back to the ‘hidden’ charge-SU(2) symmetry of the model which is explicitly broken off half-filling and gives rise to a massive collective excitation, even for arbitrary higher-dimensional but bipartite lattices.
Duality Between Spin Networks and the 2D Ising Model
Bonzom, Valentin; Costantino, Francesco; Livine, Etera R.
2016-06-01
The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a fermionic and a bosonic Gaussian integral formulation for each of these functions and we show that they are the inverse of each other (up to some explicit constants) by exhibiting a supersymmetry relating the two formulations. We investigate three aspects and applications of this duality. First, we propose higher order supersymmetric theories that couple the geometry of the spin networks to the Ising model and for which supersymmetric localization still holds. Secondly, after interpreting the generating function of spin network evaluations as the projection of a coherent state of loop quantum gravity onto the flat connection state, we find the probability distribution induced by that coherent state on the edge spins and study its stationary phase approximation. It is found that the stationary points correspond to the critical values of the couplings of the 2D Ising model, at least for isoradial graphs. Third, we analyze the mapping of the correlations of the Ising model to spin network observables, and describe the phase transition on those observables on the hexagonal lattice. This opens the door to many new possibilities, especially for the study of the coarse-graining and continuum limit of spin networks in the context of quantum gravity.
Effects of Agent's Repulsion in 2d Flocking Models
Moussa, Najem; Tarras, Iliass; Mazroui, M'hammed; Boughaleb, Yahya
In nature many animal groups, such as fish schools or bird flocks, clearly display structural order and appear to move as a single coherent entity. In order to understand the complex behavior of these systems, many models have been proposed and tested so far. This paper deals with an extension of the Vicsek model, by including a second zone of repulsion, where each agent attempts to maintain a minimum distance from the others. The consideration of this zone in our study seems to play an important role during the travel of agents in the two-dimensional (2D) flocking models. Our numerical investigations show that depending on the basic ingredients such as repulsion radius (R1), effect of density of agents (ρ) and noise (η), our nonequilibrium system can undergo a kinetic phase transition from no transport to finite net transport. For different values of ρ, kinetic phase diagrams in the plane (η ,R1) are found. Implications of these findings are discussed.
Magnetic and pair correlations of the Hubbard model with next-nearest-neighbor hopping
A combination of analytical approaches and quantum Monte Carlo simulations is used to study both magnetic and pairing correlations for a version of the Hubbard model that includes second-neighbor hopping t'=-0.35t as a model for high-temperature superconductors. Magnetic properties are analyzed using the two-particle self-consistent approach. The maximum in magnetic susceptibility as a function of doping appears both at finite t' and at t'=0 but for two totally different physical reasons. When t'=0, it is induced by antiferromagnetic correlations while at t'=-0.35t it is a band structure effect amplified by interactions. Finally, pairing fluctuations are compared with T-matrix results to disentangle the effects of van Hove singularity and of nesting on superconducting correlations. The addition of antiferromagnetic fluctuations increases slightly the d-wave superconducting correlations despite the presence of a van Hove singularity which tends to decrease them in the repulsive model. Some aspects of the phase diagram and some subtleties of finite-size scaling in Monte Carlo simulations, such as inverted finite-size dependence, are also discussed
Mott-insulator phase of the one-dimensional Bose-Hubbard model: A high-order perturbative study
The one-dimensional Bose-Hubbard model at a unit filling factor is studied by means of a very high-order symbolic perturbative expansion. Analytical expressions are derived for the ground-state quantities such as energy per site, variance of on-site occupation, and correlation functions: j†aj+r> and jnj+r>. These findings are compared to numerics and good agreement is found in the Mott insulator phase. Our results provide analytical approximations to important observables in the Mott phase, and are also of direct relevance to future experiments with ultracold atomic gases placed in optical lattices. We also discuss the symmetry of the Bose-Hubbard model associated with the sign change of the tunneling coupling
Kumar, Manoranjan; Soos, Zolt'an G.
2011-01-01
The bond order wave (BOW) phase of the extended Hubbard model (EHM) in one dimension (1D) is characterized at intermediate correlation $U = 4t$ by exact treatment of $N$-site systems. Linear coupling to lattice (Peierls) phonons and molecular (Holstein) vibrations are treated in the adiabatic approximation. The molar magnetic susceptibility $\\chi_M(T)$ is obtained directly up to $N = 10$. The goal is to find the consequences of a doubly degenerate ground state (gs) and finite magnetic gap $E_...
Properties of the one-dimensional Bose-Hubbard model from a high-order perturbative expansion
Damski, Bogdan; Zakrzewski, Jakub
2015-01-01
We employ a high-order perturbative expansion to characterize the ground state of the Mott phase of the one-dimensional Bose-Hubbard model. We compute for different integer filling factors the energy per lattice site, the two-point and density-density correlations, and expectation values of powers of the on-site number operator determining the local atom number fluctuations (variance, skewness, kurtosis). We compare these expansions to numerical simulations of the infinite-size system to dete...
The Mott insulator phase of the one dimensional Bose-Hubbard model: a high order perturbative study
Damski, Bogdan; Zakrzewski, Jakub
2006-01-01
The one dimensional Bose-Hubbard model at a unit filling factor is studied by means of a very high order symbolic perturbative expansion. Analytical expressions are derived for the ground state quantities such as energy per site, variance of on-site occupation, and different correlation functions. These findings are compared to numerics and good agreement is found in the Mott insulator phase. Our results provide analytical approximations to important observables in the Mott phase, and are als...
Ab initio modeling of 2D layered organohalide lead perovskites
Fraccarollo, Alberto; Cantatore, Valentina; Boschetto, Gabriele; Marchese, Leonardo; Cossi, Maurizio
2016-04-01
A number of 2D layered perovskites A2PbI4 and BPbI4, with A and B mono- and divalent ammonium and imidazolium cations, have been modeled with different theoretical methods. The periodic structures have been optimized (both in monoclinic and in triclinic systems, corresponding to eclipsed and staggered arrangements of the inorganic layers) at the DFT level, with hybrid functionals, Gaussian-type orbitals and dispersion energy corrections. With the same methods, the various contributions to the solid stabilization energy have been discussed, separating electrostatic and dispersion energies, organic-organic intralayer interactions and H-bonding effects, when applicable. Then the electronic band gaps have been computed with plane waves, at the DFT level with scalar and full relativistic potentials, and including the correlation energy through the GW approximation. Spin orbit coupling and GW effects have been combined in an additive scheme, validated by comparing the computed gap with well known experimental and theoretical results for a model system. Finally, various contributions to the computed band gaps have been discussed on some of the studied systems, by varying some geometrical parameters and by substituting one cation in another's place.
Phonon-like excitations in the two-state Bose-Hubbard model
I.V. Stasyuk
2015-12-01
Full Text Available The spectrum of phonon-like collective excitations in the system of Bose-atoms in optical lattice (more generally, in the system of quantum particles described by the Bose-Hubbard model is investigated. Such excitations appear due to displacements of particles with respect to their local equilibrium positions. The two-level model taking into account the transitions of bosons between the ground state and the first excited state in potential wells, as well as interaction between them, is used. Calculations are performed within the random phase approximation in the hard-core boson limit. It is shown that excitation spectrum in normal phase consists of the one exciton-like band, while in the phase with BE condensate an additional band appears. The positions, spectral weights and widths of bands strongly depend on chemical potential of bosons and temperature. The conditions of stability of a system with respect to the lowering of symmetry and displacement modulation are discussed.
The method of evaluating quantum partition function for the Hubbard model
The method of evaluation of quantum partition function (QPF) in some four fermion models is proposed. The calculations are carried out by the path integral method. The integral is evaluated by introducing the additional fields (called Hubbard-Stratanovich transformation in some models), integration over fermionic variables, and considering the finite-dimensional approximation of rest integral over bosonic fields in the infinite limit. The result can be represented as a sum of the functional derivatives with respect to the arbitrary bosonic field of the quantum partition of free fermionic theory in the external bosonic field. This expression can be treated in a mean field approximation in closed form (the determinants corresponding to the arbitrary external field are substituted by its mean values corresponding to the mean value of the external fields). The quantum partition function is represented as the integral representation of the function. The approximation for the QPF of the free theory is considered, and the corresponding answer for QPF is studied. A convenient perturbation expansion for ln Z is developed. (author). 6 refs, 1 fig
Solving the parquet equations for the Hubbard model beyond weak coupling.
Tam, Ka-Ming; Fotso, H; Yang, S-X; Lee, Tae-Woo; Moreno, J; Ramanujam, J; Jarrell, M
2013-01-01
We find that imposing crossing symmetry in the iteration process considerably extends the range of convergence for solutions of the parquet equations for the Hubbard model. When crossing symmetry is not imposed, the convergence of both simple iteration and more complicated continuous loading (homotopy) methods is limited to high temperatures and weak interactions. We modify the algorithm to impose the crossing symmetry without increasing the computational complexity. We also imposed time reversal and a subset of the point group symmetries, but they did not further improve the convergence. We elaborate the details of the latency hiding scheme which can significantly improve the performance in the computational implementation. With these modifications, stable solutions for the parquet equations can be obtained by iteration more quickly even for values of the interaction that are a significant fraction of the bandwidth and for temperatures that are much smaller than the bandwidth. This may represent a crucial step towards the solution of two-particle field theories for correlated electron models. PMID:23410464
Study of the multi-orbital Hubbard model at finite temperature
Mukherjee, Anamitra; Dong, Shuai; Alvarez, Gonzalo; Dagotto, Elbio
2014-03-01
Research in pnictide superconductors have clearly established the need for the study of multi-orbital Hubbard models. With this motivation, here we apply a combination of the real-space Exact Diagonalization and Classical Monte Carlo (ED+MC) method, widely used in manganites, with the standard Hartree-Fock mean field (MF) theory to investigate the properties of multiorbital models as a function of temperature. In this approach the MF parameters are treated via a classical MC and the fermions moving in the MF background are solved by exact diagonalization. The temperature dependence of the dynamical spin susceptibility S(q --> , ω) , orbital resolved single particle spectral function A(k --> , ω) , optical conductivity, and real space charge/spin/orbital density maps are calculated at different dopings. These results are relevant in understanding the role of the multiple degrees of freedom in governing the magnetic and transport properties of the Fe based superconductor materials. Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA.
Robust Supersolidity in the V1- V2 Extended Bose-Hubbard Model
Greene, Nicole; Pixley, Jedediah
2016-05-01
Motivated by ultra-cold atomic gases with long-range interactions in an optical lattice we study the effects of the next-nearest neighbor interaction on the extended Bose-Hubbard model on a square lattice. Using the variational Gutzwiller approach with a four-site unit cell we determine the ground state phase diagrams as a function of the model parameters. We focus on the interplay of each interaction between the nearest neighbor (V1) , the next-nearest neighbor (V2) , and the onsite repulsion (U). We find various super-solid phases that can be described by one of the ordering wave-vectors (π, 0), (0, π) , and (π, π) . In the limits V1, V2 U we find phases reminiscent of the limit V2 = 0 but with a richer super solid structure. For V1 qualitatively new super solid phase that is quite stable and occupies a large region of the phase diagram. For sufficiently strong interactions we find various Mott and charge density wave (CDW) insulating phases that can be understood in the classical limit (i.e. no inter-site tunneling). We characterize the nature of each quantum phase transition between Mott/CDW to super-solid to superfluid at the mean field level.
Frésard, Raymond; Steffen, Kevin; Kopp, Thilo
2016-03-01
Attractive non-local interactions jointly with repulsive local interaction in a microscopic modelling of electronic Fermi liquids generate a competition between an enhancement of the static charge susceptibility–ultimately signalling charge instability and phase separation–and its correlation induced suppression. We analyse this scenario through the investigation of the extended Hubbard model on a two-dimensional square lattice, using the spin rotation invariant slave-boson representation of Kotliar and Ruckenstein. The quasiparticle density of states, the renormalised effective mass and the Landau parameter F s 0 are presented, whereby the positivity of F s 0 – 1 constitutes a criterion for stability. Van Hove singularities in the density of states support possible charge instabilities. A (negative) next-nearest neighbour hopping parameter t' shifts their positions and produces a tendency towards charge instability even for low filling whereas the t'-controlled particle-hole asymmetry of the correlation driven effective mass is small. A region of instability on account of the attractive interaction V is identified, either at half filling in the absence of strong electronic correlations or, in the case of large on-site interaction U, at densities far from half filling.
Slow dynamics in a two-dimensional Anderson-Hubbard model
Bar Lev, Yevgeny; Reichman, David R.
2016-02-01
We study the real-time dynamics of a two-dimensional Anderson-Hubbard model using nonequilibrium self-consistent perturbation theory within the second-Born approximation. When compared with exact diagonalization performed on small clusters, we demonstrate that for strong disorder this technique approaches the exact result on all available timescales, while for intermediate disorder, in the vicinity of the many-body localization transition, it produces quantitatively accurate results up to nontrivial times. Our method allows for the treatment of system sizes inaccessible by any numerically exact method and for the complete elimination of finite-size effects for the times considered. We show that for a sufficiently strong disorder the system becomes nonergodic, while for intermediate disorder strengths and for all accessible timescales transport in the system is strictly subdiffusive. We argue that these results are incompatible with a simple percolation picture, but are consistent with the heuristic random resistor network model where subdiffusion may be observed for long times until a crossover to diffusion occurs. The prediction of slow finite-time dynamics in a two-dimensional interacting and disordered system can be directly verified in future cold-atoms experiments.
Topological order in 1D super-lattice Bose-Hubbard models
Fleischhauer, Michael; Grusdt, Fabian; Hoening, Michael
2013-05-01
After the discovery of topological insulators as a new state of matter and their consequent classification for free fermions, the question arises what kind of topological order can be supported by incompressible systems of interacting bosons. We consider a 1D super-lattice Hamiltonian with a non-trivial band structure (the Su-Schrieffer-Heeger model) and show that its Mott-insulating (MI) states can be classified by a quantized many-body winding number. This quantization is protected by sub-lattice and time-reversal symmetries, and it allows the implementation of a quantized cyclic pumping process (Thouless pump) in a simple super-lattice Bose-Hubbard model (BHM). For extended BHMs we discuss a connection of such a pump with the fractional quantum Hall effect. Furthermore we show that the quantization of the winding number leads to localized, protected edge states at sharp interfaces between topologically distinct MI phases which can be experimentally realized using Bose-Fermi mixtures in optical superlattices. DMRG simulations show that these edge states manifest themself either in localized density maxima or localized density minima, which can easily be detected. Supported by research center OPTIMAS and graduate school MAINZ.
Robust Supersolidity in the V1- V2 Extended Bose-Hubbard Model
Greene, Nicole; Pixley, Jedediah
2016-05-01
Motivated by ultra-cold atomic gases with long-range interactions in an optical lattice we study the effects of the next-nearest neighbor interaction on the extended Bose-Hubbard model on a square lattice. Using the variational Gutzwiller approach with a four-site unit cell we determine the ground state phase diagrams as a function of the model parameters. We focus on the interplay of each interaction between the nearest neighbor (V1) , the next-nearest neighbor (V2) , and the onsite repulsion (U). We find various super-solid phases that can be described by one of the ordering wave-vectors (π, 0), (0, π) , and (π, π) . In the limits V1, V2 U we find phases reminiscent of the limit V2 = 0 but with a richer super solid structure. For V1
VAM2D: Variably saturated analysis model in two dimensions
This report documents a two-dimensional finite element model, VAM2D, developed to simulate water flow and solute transport in variably saturated porous media. Both flow and transport simulation can be handled concurrently or sequentially. The formulation of the governing equations and the numerical procedures used in the code are presented. The flow equation is approximated using the Galerkin finite element method. Nonlinear soil moisture characteristics and atmospheric boundary conditions (e.g., infiltration, evaporation and seepage face), are treated using Picard and Newton-Raphson iterations. Hysteresis effects and anisotropy in the unsaturated hydraulic conductivity can be taken into account if needed. The contaminant transport simulation can account for advection, hydrodynamic dispersion, linear equilibrium sorption, and first-order degradation. Transport of a single component or a multi-component decay chain can be handled. The transport equation is approximated using an upstream weighted residual method. Several test problems are presented to verify the code and demonstrate its utility. These problems range from simple one-dimensional to complex two-dimensional and axisymmetric problems. This document has been produced as a user's manual. It contains detailed information on the code structure along with instructions for input data preparation and sample input and printed output for selected test problems. Also included are instructions for job set up and restarting procedures. 44 refs., 54 figs., 24 tabs
Monte Carlo simulations of two-dimensional Hubbard models with string bond tensor-network states
Song, Jeong-Pil; Wee, Daehyun; Clay, R. T.
2015-03-01
We study charge- and spin-ordered states in the two-dimensional extended Hubbard model on a triangular lattice at 1/3 filling. While the nearest-neighbor Coulomb repulsion V induces charge-ordered states, the competition between on-site U and nearest-neighbor V interactions lead to quantum phase transitions to an antiferromagnetic spin-ordered phase with honeycomb charge order. In order to avoid the fermion sign problem and handle frustrations here we use quantum Monte Carlo methods with the string-bond tensor network ansatz for fermionic systems in two dimensions. We determine the phase boundaries of the several spin- and charge-ordered states and show a phase diagram in the on-site U and the nearest-neighbor V plane. The numerical accuracy of the method is compared with exact diagonalization results in terms of the size of matrices D. We also test the use of lattice symmetries to improve the string-bond ansatz. Work at Mississippi State University was supported by the US Department of Energy grant DE-FG02-06ER46315.
Two-state Bose-Hubbard model in the hard-core boson limit
O.V. Velychk
2011-03-01
Full Text Available Phase transition into the phase with Bose-Einstein (BE condensate in the two-band Bose-Hubbard model with the particle hopping in the excited band only is investigated. Instability connected with such a transition (which appears at excitation energies δ0|, where |t'0| is the particle hopping parameter is considered. The re-entrant behaviour of spinodales is revealed in the hard-core boson limit in the region of positive values of chemical potential. It is found that the order of the phase transition undergoes a change in this case and becomes the first one; the re-entrant transition into the normal phase does not take place in reality. First order phase transitions also exist at negative values of δ (under the condition δ>δcrit≈ − 0.12|t'0|. At μ0|, μ phase diagrams are built and localizations of tricritical points are established. The conditions are found at which the separation on the normal phase and the phase with the BE condensate takes place.
Sato, Ryo; Yokoyama, Hisatoshi
2016-07-01
Band renormalization effects (BRE) are comprehensively studied for a mixed state of dx2 - y2-wave superconducting (d-SC) and antiferromagnetic (AF) orders, in addition to simple d-SC, AF, and normal (paramagnetic) states, by applying a variational Monte Carlo method to a two-dimensional Hubbard (t-t'-U) model. In a weakly correlated regime (U/t ≲ 6), BRE are negligible on all the states studied. As previously shown, the effective band of d-SC is greatly renormalized but the modifications of physical quantities, including energy improvement, are negligible. In contrast, BRE on the AF state considerably affects various features of the system. Because the energy is markedly improved for t'/t t'{L} [t' t'{L}, because the existence of Fermi surfaces near (π ,0) is a requisite for the electron scattering of {q} = (π ,π ). Actually, the coexistent state appears mainly for t'{L}/t < t'/t ≲ 0.2 in the mixed state. Nevertheless, the AF and coexisting states become unstable toward phase separation for - 0.05 ≲ t'/t ≲ 0.2 but become stable at other values of t'/t owing to the energy reduction by the diagonal hopping of doped holes. We show that this instability does not directly correlate with the strength of d-SC.
Antiferromagnetism in three-band Hubbard model: Local-ansatz approach
The ground state of the three-band Hubbard Hamiltonian for CuO2 planes of high-Tc superconductors is investigated. Correlations between holes are included by a local-ansatz approach which starts from the Hartree-Fock approximation and emphasizes the local character of hole correlations. It is found that the hole distribution within CuO2 planes and the region of stability of an antiferromagnetic (AF) ground state are significantly modified by hole correlations. At the filling of one hole per CuO2 unit, and for realistic parameters, the ground state exhibits an AF long-range order. Taking into account the effect of quantum fluctuations, the magnetic moment amounts to 0.47μB which agrees very well with the experimental value for La2CuO4. The order parameter decreases with doping and disappears for the doping of 0.06 hole per unit cell. It is found that the nearest-neighbor oxygen hopping destabilizes AF ground state which proves the importance of this parameter for quantitative analysis. A favorable comparison between the present results and those obtained within variational Monte Carlo, as well as within the Gutzwiller approximation for a similar model, is presented
Antiferromagnetism in three-band Hubbard model: Local-ansatz approach
Dutka, J.; Oles, A.M. (Institute of Physics, Jagellonian University, Reymonta 4, PL-30-059 Krakow, Poland (PL))
1991-03-01
The ground state of the three-band Hubbard Hamiltonian for CuO{sub 2} planes of high-{ital T}{sub {ital c}} superconductors is investigated. Correlations between holes are included by a local-ansatz approach which starts from the Hartree-Fock approximation and emphasizes the local character of hole correlations. It is found that the hole distribution within CuO{sub 2} planes and the region of stability of an antiferromagnetic (AF) ground state are significantly modified by hole correlations. At the filling of one hole per CuO{sub 2} unit, and for realistic parameters, the ground state exhibits an AF long-range order. Taking into account the effect of quantum fluctuations, the magnetic moment amounts to 0.47{mu}{sub {ital B}} which agrees very well with the experimental value for La{sub 2}CuO{sub 4}. The order parameter decreases with doping and disappears for the doping of 0.06 hole per unit cell. It is found that the nearest-neighbor oxygen hopping destabilizes AF ground state which proves the importance of this parameter for quantitative analysis. A favorable comparison between the present results and those obtained within variational Monte Carlo, as well as within the Gutzwiller approximation for a similar model, is presented.
Superconducting fluctuations in the normal state of the two-dimensional Hubbard model.
Chen, Xi; LeBlanc, J P F; Gull, Emanuel
2015-09-11
We compute the two-particle quantities relevant for superconducting correlations in the two-dimensional Hubbard model within the dynamical cluster approximation. In the normal state we identify the parameter regime in density, interaction, and second-nearest-neighbor hopping strength that maximizes the d_{x^{2}-y^{2}} superconducting transition temperature. We find in all cases that the optimal transition temperature occurs at intermediate coupling strength, and is suppressed at strong and weak interaction strengths. Similarly, superconducting fluctuations are strongest at intermediate doping and suppressed towards large doping and half filling. We find a change in sign of the vertex contributions to d_{xy} superconductivity from repulsive near half filling to attractive at large doping. p-wave superconductivity is not found at the parameters we study, and s-wave contributions are always repulsive. For negative second-nearest-neighbor hopping the optimal transition temperature shifts towards the electron-doped side in opposition to the van Hove singularity, which moves towards hole doping. We surmise that an increase of the local interaction of the electron-doped compounds would increase T_{c}. PMID:26406843
Orbital nematic order and interplay with magnetism in the two-orbital Hubbard model
Motivated by the recent angle-resolved photoemission spectroscopy (ARPES) on FeSe and iron pnictide families of iron-based superconductors, we have studied the orbital nematic order and its interplay with antiferromagnetism within the two-orbital Hubbard model. We used random phase approximation (RPA) to calculate the dependence of the orbital and magnetic susceptibilities on the strength of interactions and electron density (doping). To account for strong electron correlations not captured by RPA, we further employed non-perturbative variational cluster approximation (VCA) capable of capturing symmetry broken magnetic and orbitally ordered phases. Both approaches show that the electron and hole doping affect the two orders differently. While hole doping tends to suppress both magnetism and orbital ordering, the electron doping suppresses magnetism faster. Crucially, we find a realistic parameter regime for moderate electron doping that stabilizes orbital nematicity in the absence of long-range antiferromagnetic order. This is reminiscent of the non-magnetic orbital nematic phase observed recently in FeSe and a number of iron pnictide materials and raises the possibility that at least in some cases, the observed electronic nematicity may be primarily due to orbital rather than magnetic fluctuations. (paper)
Quantum Monte Carlo simulation study of two-dimensional Hubbard model
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)
Application of a multisite mean-field theory to the disordered Bose-Hubbard model
We present a multisite formulation of mean-field theory applied to the disordered Bose-Hubbard model. In this approach the lattice is partitioned into clusters, each isolated cluster being treated exactly, with intercluster hopping being treated approximately. The theory allows for the possibility of a different superfluid order parameter at every site in the lattice, such as what has been used in previously published site-decoupled mean-field theories, but a multisite formulation also allows for the inclusion of spatial correlations allowing us, e.g., to calculate the correlation length (over the length scale of each cluster). We present our numerical results for a two-dimensional system. This theory is shown to produce a phase diagram in which the stability of the Mott-insulator phase is larger than that predicted by site-decoupled single-site mean-field theory. Two different methods are given for the identification of the Bose-glass-to-superfluid transition, one an approximation based on the behavior of the condensate fraction, and one that relies on obtaining the spatial variation of the order parameter correlation. The relation of our results to a recent proposal that both transitions are non-self-averaging is discussed.
Importance of Overpressure in 2D Gas Hydrate Modeling
Hauschildt, J.; Unnithan, V.
2005-12-01
Numerical models for sub-seafloor gas hydrate formation [1],[2],[3] which describe the driving fluid transport processes only in the vertical direction, restrict the computationally expensive problem to one dimension. This assumption is only valid in regions where permeable sediments induce no overpressure and where there is little lateral variation of physical properties and boundary conditions. Local accumulations of gas hydrates or authigenic carbonates can significantly reduce the porosity and permeability. In combination with topographic and structural features, subtle but important deviations from the 1D model are considered to occur. This poster shows results obtained from a 2D finite difference model developed for describing the evolution of the gas hydrate zone in structurally complex areas. The discretisation of the terms governing the thermodynamic and transport processes is implemented explicitely in time for the advection and diffusion processes, but implicitely for phase transitions. Although the time scales for transport and phase transitions can differ by several orders of magnitude, this scheme allows for an efficient computation for model runs both over the system's equilibration period in the order of 107 yr or to resolve the effects of sea-level changes within 103 yr. A sensitivity analysis confines the parameter space relevant for hydrate formation influenced by lateral fluid flow, and results for the predicted deviations from a multi-1D model for high gas hydrate fractions and fluid flow rates are presented. References [1] M.K. Davie and B.A. Buffett. Sources of methane for marine gas hydrate: inferences from a comparison of observations and numerical models. Earth and Planetary Science Letters, 206:51-63, 2003. [2] W. Xu and C. Ruppell. Predicting the occurrence, distribution, and evolution of methane hydrate in porous marine sediments. Journal of Geohphysical Research, (B3):5081-5095, 1999. [3] J.B. Klauda and S.I. Sandler. Predictions of
Dynamics of fermionic Hubbard models after interaction quenches in one and two dimensions
Hamerla, Simone Anke
2013-10-15
In the last years the impressive progress on the experimental side led to a variety of new experiments allowing to address systems out of equilibrium. In this way the behavior of such systems far from equilibrium is no longer a purely theoretical issue but indeed observable. New experimental techniques, like particles trapped in optical lattices, render a realization of quantum systems with nearly arbitrary system parameters possible and provide a possibility to study their time evolution. Systems out of equilibrium are characterized by the fact, that these systems are in highly excited states giving rise to totally new fascinating properties. In the present thesis one- and two-dimensional fermionic Hubbard models out of equilibrium are discussed. The system is taken out of equilibrium by a so-called interaction quench. At the beginning the system is prepared in the groundstate of the non-interacting Hamiltonian. At a time t the interaction between the fermions is suddenly turned on so that the time evolution is governed by the whole, interacting Hamiltonian. Hence the system is prepared in the groundstate of one Hamiltonian but evolves according to a different Hamiltonian. Consequently the system ends up in a highly excited state. To describe such a system a method based on an expansion of the Heisenberg equations of motion to highest order possible is developed in this thesis. This method provides an exact description of the time evolution on short and intermediate time scales after the quench. As the method reveal exact results and does not rely on any perturbative assumption, a study of arbitrarily large interaction strengths is possible. Besides, the method is one of the few methods capable of two-dimensional systems. In the following the method used in this thesis is explained and advantages and disadvantages of the approach are thematized. For this purpose the results of the developed iterated equation of motion approach are compared to results obtained in
Split Hubbard bands at low densities
Hansen, Daniel; Perepelitsky, Edward; Shastry, B. Sriram
2011-05-01
We present a numerical scheme for the Hubbard model that throws light on the rather esoteric nature of the upper and lower Hubbard bands, which have been invoked often in literature. We present a self-consistent solution of the ladder-diagram equations for the Hubbard model, and show that these provide, at least in the limit of low densities of particles, a vivid picture of the Hubbard split bands. We also address the currently topical problem of decay of the doublon states that are measured in optical trap studies, using both the ladder scheme and also an exact two-particle calculation of a relevant Green’s function.
Janani, C.; Merino, J.; McCulloch, I. P.; Powell, B. J.
2014-01-01
Motivated by Mo$_3$S$_7$(dmit)$_3$, we investigate the Hubbard model on the triangular necklace lattice at two-thirds filling. We show, using second order perturbation theory, that in the molecular limit, the ground state and the low energy excitations of this model are identical to those of the spin-one Heisenberg chain. The latter model is known to be in the symmetry protected topological Haldane phase. Away from this limit we show, on the basis of symmetry arguments and density matrix reno...
The Bose glass (BG) phase is the Griffiths region of the disordered Bose–Hubbard model (BHM), characterized by finite, quasi-superfluid clusters within a Mott insulating background. We propose to utilize this characterization to identify the complete zero-temperature phase diagram of the disordered BHM in d ⩾ 2 dimensions by analysing the geometric properties of what we call superfluid (SF) clusters, which are defined to be clusters of sites with non-integer expectation values for the local boson occupation number. The Mott insulator phase then is the region in the phase diagram where no SF clusters exist, and the SF phase the region where SF clusters percolate—the BG phase is inbetween: SF clusters exist, but do not percolate. This definition is particularly useful in the context of local mean field (LMF) or Gutzwiller–Ansatz calculations, where we show that an identification of the phases on the basis of global quantities such as the averaged SF order parameter and the compressibility is misleading. We apply the SF cluster analysis to the LMF ground states of the two-dimensional disordered BHM to produce its phase diagram and find (a) an excellent agreement with the phase diagram predicted on the basis of quantum Monte Carlo simulations for the commensurate density n = 1 and (b) large differences to stochastic mean field and other mean field predictions for fixed disorder strength. The relation of the percolation transition of the SF clusters with the onset of non-vanishing SF stiffness indicating the BG to SF transition is discussed. (paper)
A 2D simulation model for urban flood management
Price, Roland; van der Wielen, Jonathan; Velickov, Slavco; Galvao, Diogo
2014-05-01
The European Floods Directive, which came into force on 26 November 2007, requires member states to assess all their water courses and coast lines for risk of flooding, to map flood extents and assets and humans at risk, and to take adequate and coordinated measures to reduce the flood risk in consultation with the public. Flood Risk Management Plans are to be in place by 2015. There are a number of reasons for the promotion of this Directive, not least because there has been much urban and other infrastructural development in flood plains, which puts many at risk of flooding along with vital societal assets. In addition there is growing awareness that the changing climate appears to be inducing more frequent extremes of rainfall with a consequent increases in the frequency of flooding. Thirdly, the growing urban populations in Europe, and especially in the developing countries, means that more people are being put at risk from a greater frequency of urban flooding in particular. There are urgent needs therefore to assess flood risk accurately and consistently, to reduce this risk where it is important to do so or where the benefit is greater than the damage cost, to improve flood forecasting and warning, to provide where necessary (and possible) flood insurance cover, and to involve all stakeholders in decision making affecting flood protection and flood risk management plans. Key data for assessing risk are water levels achieved or forecasted during a flood. Such levels should of course be monitored, but they also need to be predicted, whether for design or simulation. A 2D simulation model (PriceXD) solving the shallow water wave equations is presented specifically for determining flood risk, assessing flood defense schemes and generating flood forecasts and warnings. The simulation model is required to have a number of important properties: -Solve the full shallow water wave equations using a range of possible solutions; -Automatically adjust the time step and
Phase transitions in Bose-Fermi-Hubbard model in the heavy fermion limit: Hard-core boson approach
I.V. Stasyuk
2015-12-01
Full Text Available Phase transitions are investigated in the Bose-Fermi-Hubbard model in the mean field and hard-core boson approximations for the case of infinitely small fermion transfer and repulsive on-site boson-fermion interaction. The behavior of the Bose-Einstein condensate order parameter and grand canonical potential is analyzed as functions of the chemical potential of bosons at zero temperature. The possibility of change of order of the phase transition to the superfluid phase in the regime of fixed values of the chemical potentials of Bose- and Fermi-particles is established. The relevant phase diagrams are built.
Properties of the one-dimensional Bose-Hubbard model from a high-order perturbative expansion
Damski, Bogdan; Zakrzewski, Jakub
2015-12-01
We employ a high-order perturbative expansion to characterize the ground state of the Mott phase of the one-dimensional Bose-Hubbard model. We compute for different integer filling factors the energy per lattice site, the two-point and density-density correlations, and expectation values of powers of the on-site number operator determining the local atom number fluctuations (variance, skewness, kurtosis). We compare these expansions to numerical simulations of the infinite-size system to determine their range of applicability. We also discuss a new sum rule for the density-density correlations that can be used in both equilibrium and non-equilibrium systems.
Paul, Saurabh; Johnson, P R; Tiesinga, Eite
2016-01-01
We show that for ultra-cold neutral bosonic atoms held in a three-dimensional periodic potential or optical lattice, a Hubbard model with dominant, attractive three-body interactions can be generated. In fact, we derive that the effect of pair-wise interactions can be made small or zero starting from the realization that collisions occur at the zero-point energy of an optical lattice site and the strength of the interactions is energy dependent from effective-range contributions. We determine...
How to control pairing fluctuations: SU(2) slave-rotor gauge theory of the Hubbard model
Kim, Ki-Seok
2006-01-01
We study how to incorporate Mott physics in the BCS-type superconductor, motivated from the fact that high $T_c$ superconductivity results from a Mott insulator via hole doping. The U(1) slave-rotor representation was proposed to take local density fluctuations into account non-perturbatively, describing the Mott-Hubbard transition at half filling. Since this decomposition cannot control local pairing fluctuations, the U(1) slave-rotor representation does not give a satisfactory treatment for...
Phase separation instabilities and magnetism in two dimensional square and honeycomb Hubbard model
The variational cluster approximation is applied to rigorously calculate intrinsic local electron correlations in bipartite square and honeycomb Hubbard lattices. The Mott–Hubbard gap at half filling is manifested by a smooth metal–insulator transition in both lattices in agreement with the generic two-dimensional phase diagram. However, a density variation with the chemical potential shows the distinct structural differences away from half filling. The square lattice exhibits electron density discontinuity accompanied with spontaneous transition from antiferromagnetic Mott–Hubbard insulator into nonmagnetic metal. The spectral density anomaly and spin susceptibility peaks also are signaling on coexistence of hole rich metallic and hole poor insulating regions. In contrast, honeycomb lattice does not show density anomaly but displays a smooth transition with continuous evolution of a homogenous metallic state. These calculations provide strong evidence for spontaneous phase separation instability found in our quantum cluster calculations at moderate U - Highlights: • Variational cluster approximation (VCA) captures phase separation in various lattices under doping. • The conditions are formulated for continuous and discontinuous transitions. • Discontinuous phase separation is found in square lattices under doping and pressure. • Honeycomb lattice displays continuous evolution of a homogenous metallic state. • Spectral function anomaly in square geometry displays the folding of the first Brillouin zone
The Implementation of C-ID, R2D2 Model on Learning Reading Comprehension
Rayanto, Yudi Hari; Rusmawan, Putu Ngurah
2016-01-01
The purposes of this research are to find out, (1) whether C-ID, R2D2 model is effective to be implemented on learning Reading comprehension, (2) college students' activity during the implementation of C-ID, R2D2 model on learning Reading comprehension, and 3) college students' learning achievement during the implementation of C-ID, R2D2 model on…
Le modele de Hubbard bidimensionnel a faible couplage: Thermodynamique et phenomenes critiques
Roy, Sebastien
Une etude systematique du modele de Hubbard en deux dimensions a faible couplage a l'aide de la theorie Auto-Coherente a Deux Particules (ACDP) dans le diagramme temperature-dopage-interaction-sauts permet de mettre en evidence l'influence des fluctuations magnetiques sur les proprietes thermodynamiques du systeme electronique sur reseau. Le regime classique renormalise a temperature finie pres du dopage nul est marque par la grandeur de la longueur de correlation de spin comparee a la longueur thermique de de Broglie et est caracterisee par un accroissement drastique de la longueur de correlation de spin. Cette croissance exponentielle a dopage nul marque la presence d'un pic de chaleur specifique en fonction de la temperature a basse temperature. Une temperature de crossover est alors associee a la temperature a laquelle la longueur de correlation de spin est egale a la longueur thermique de de Broglie. C'est a cette temperature caracteristique, ou est observee l'ouverture du pseudogap dans le poids spectral, que se situe le maximum du pic de chaleur specifique. La presence de ce pic a des consequences sur l'evolution du potentiel chimique avec le dopage lorsque l'uniformite thermodynamique est respectee. Les contraintes imposees par les lois de la thermodynamique font en sorte que l'evolution du potentiel chimique avec le dopage est non triviale. On demontre entre autres que le potentiel chimique est proportionnel a la double occupation qui est reliee au moment local. Par ailleurs, une derivation de la fonction de mise a l'echelle de la susceptibilite de spin a frequence nulle au voisinage d'un point critique marque sans equivoque la presence d'un point critique quantique en dopage pour une valeur donnee de l'interaction. Ce point critique, associe a une transition de phase magnetique en fonction du dopage a temperature nulle, induit un comportement non trivial sur les proprietes physiques du systeme a temperature finie. L'approche quantitative ACDP permet de
Chae, Dongho; Constantin, Peter; Wu, Jiahong
2014-09-01
We give an example of a well posed, finite energy, 2D incompressible active scalar equation with the same scaling as the surface quasi-geostrophic equation and prove that it can produce finite time singularities. In spite of its simplicity, this seems to be the first such example. Further, we construct explicit solutions of the 2D Boussinesq equations whose gradients grow exponentially in time for all time. In addition, we introduce a variant of the 2D Boussinesq equations which is perhaps a more faithful companion of the 3D axisymmetric Euler equations than the usual 2D Boussinesq equations.
Dallaire-Demers, Pierre-Luc; Wilhelm, Frank K.
2016-03-01
Many phenomena of strongly correlated materials are encapsulated in the Fermi-Hubbard model whose thermodynamic properties can be computed from its grand-canonical potential. In general, there is no closed-form expression of the grand-canonical potential for lattices of more than one spatial dimension, but solutions can be numerically approximated using cluster methods. To model long-range effects such as order parameters, a powerful method to compute the cluster's Green's function consists of finding its self-energy through a variational principle. This allows the possibility of studying various phase transitions at finite temperature in the Fermi-Hubbard model. However, a classical cluster solver quickly hits an exponential wall in the memory (or computation time) required to store the computation variables. Here it is shown theoretically that the cluster solver can be mapped to a subroutine on a quantum computer whose quantum memory usage scales linearly with the number of orbitals in the simulated cluster and the number of measurements scales quadratically. A quantum computer with a few tens of qubits could therefore simulate the thermodynamic properties of complex fermionic lattices inaccessible to classical supercomputers.
Two-component Bose-Hubbard model with higher-angular-momentum states
Pietraszewicz, Joanna; Sowiński, Tomasz; Brewczyk, Mirosław; Zakrzewski, Jakub; Lewenstein, Maciej; Gajda, Mariusz
2012-05-01
Bose-Hubbard Hamiltonian of cold two-component Bose gas of spinor chromium atoms is studied. Dipolar interactions of magnetic moments while tuned resonantly by an ultralow magnetic field can lead to a transfer of atoms from the ground to excited Wannier states with a nonvanishing angular orbital momentum. Hence we propose the way of creating Px+iPy orbital superfluid. The spin introduces an additional degree of control and leads to a variety of different stable phases of the system. The Mott insulator of atoms in a superposition of the ground and vortex Wannier states as well as a superposition of the Mott insulator with orbital superfluid are predicted.
The selection of soil models parameters in Plaxis 2D
O.V. Sokolova
2014-06-01
Full Text Available Finite element method is often used to solve complex geotechnical problems. The application of FEM-based programs demands special attention to setting models parameters and simulating soil behavior. The paper considers the problem of the model selection to describe the behavior of soils when calculating soil settlement in the check task, referring to complicated geotechnical conditions of Saint Petersburg. The obtained settlement values in Linear Elastic model, Mohr – Coulomb model, Hardening Soil model and Hardening Soil Small model were compared. The paper presents results of calibrating parameters for a geotechnical model obtained on the data of compression testing. The necessity of prior calculations to evaluate the accuracy of a soil model is confirmed.
Spiral magnetism in the single-band Hubbard model: the Hartree–Fock and slave-boson approaches
The ground-state magnetic phase diagram is investigated within the single-band Hubbard model for square and different cubic lattices. The results of employing the generalized non-correlated mean-field (Hartree–Fock) approximation and generalized slave-boson approach by Kotliar and Ruckenstein with correlation effects included are compared. We take into account commensurate ferromagnetic, antiferromagnetic, and incommensurate (spiral) magnetic phases, as well as phase separation into magnetic phases of different types, which was often lacking in previous investigations. It is found that the spiral states and especially ferromagnetism are generally strongly suppressed up to non-realistically large Hubbard U by the correlation effects if nesting is absent and van Hove singularities are well away from the paramagnetic phase Fermi level. The magnetic phase separation plays an important role in the formation of magnetic states, the corresponding phase regions being especially wide in the vicinity of half-filling. The details of non-collinear and collinear magnetic ordering for different cubic lattices are discussed. (paper)
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...
Modeling Overlapping Laminations in Magnetic Core Materials Using 2-D Finite-Element Analysis
Jensen, Bogi Bech; Guest, Emerson David; Mecrow, Barrie C.
2015-01-01
This paper describes a technique for modeling overlapping laminations in magnetic core materials using two-dimensional finite-element (2-D FE) analysis. The magnetizing characteristic of the overlapping region is captured using a simple 2-D FE model of the periodic overlapping geometry and a comp...
Kuno, Yoshihito; Sakane, Shinya; Kasamatsu, Kenichi; Ichinose, Ikuo; Matsui, Tetsuo
2016-01-01
In this paper, we study atomic quantum simulations of $(1+1)$-dimensional($(1+1)$D) U(1) gauge-Higgs models (GHMs) defined on a lattice. We explain how U(1) lattice GHMs appear from an extended Bose-Hubbard model (EBHM) describing ultra-cold atoms with a nearest neighbor repulsion in a 1D optical lattice. We first study a phase diagram of the 1D EBHM at low fillings by means of a quantum Monte-Carlo(MC) simulation. Next, we study the EBHM at large fillings and also GHMs by the MC simulations in the path-integral formalism and show that there are four phases, i.e., the Higgs phase(superfluid), the confinement phase (Mott insulator), and phases corresponding to the density wave and the supersolid. With the obtained phase diagrams, we investigate the relationship between the two models. Finally, we study real-time dynamic of an electric flux in the GHMs by the Gross-Pitaevskii equations and the truncated Wigner approximation.
2D semiclassical model for high harmonic generation from gas
陈黎明; 余玮; 张杰; 陈朝阳; 江文勉
2000-01-01
The electron behavior in laser field is described in detail. Based on the 1D semiclassical model, a 20 semiclassical model is proposed analytically using 3D DC-tunneling ionization theory. Lots of harmonic features are explained by this model, including the analytical demonstration of the maximum electron energy 3.17 Up. Finally, some experimental phenomena such as the increase of the cutoff harmonic energy with the decrease of pulse duration and the "anomalous" fluctuations in the cutoff region are explained by this model.
2-D Model Test Study of the Suape Breakwater, Brazil
Andersen, Thomas Lykke; Burcharth, Hans F.; Sopavicius, A.;
This report deals with a two-dimensional model test study of the extension of the breakwater in Suape, Brazil. One cross-section was tested for stability and overtopping in various sea conditions. The length scale used for the model tests was 1:35. Unless otherwise specified all values given in...
2D modelling and assessment of divertor performance for ITER
The results of the ITER divertor modelling performed during the EDA are summarised in the paper. Studies on the operating window and optimisation of the divertor geometry are presented together with preliminary results on the start-up limiter performance. The issue of model validation against the experimental data which is crucial for extrapolation to ITER is also addressed. (author)
Practical aspects of a 2-D edge-plasma model
The poloidal divertor configuration is considered the most promising solution to the particle and energy exhaust problem for a tokamak reactor. The scrape-off layer plasma surrounding the core and the high-recycling plasma near the divertor plates can be modelled by fluid equations for particle, momentum and energy transport. A numerical code (B2) based on a two-dimensional multi-fluid model has been developed for the study of edge plasmas in tokamaks. In this report we identify some key features of this model as applied to the DIII-D tokamak. 2 refs., 1 fig
Vibration induced flow in hoppers: DEM 2D polygon model
无
2008-01-01
A two-dimensional discrete element model (DEM) simulation of cohesive polygonal particles has been developed to assess the benefit of point source vibration to induce flow in wedge-shaped hoppers. The particle-particle interaction model used is based on a multi-contact principle.The first part of the study investigated particle discharge under gravity without vibration to determine the critical orifice size (Be) to just sustain flow as a function of particle shape. It is shown that polygonal-shaped particles need a larger orifice than circular particles. It is also shown that Be decreases as the number of particle vertices increases. Addition of circular particles promotes flow of polygons in a linear manner.The second part of the study showed that vibration could enhance flow, effectively reducing Be. The model demonstrated the importance of vibrator location (height), consistent with previous continuum model results, and vibration amplitude in enhancing flow.
Percolation properties of the 2D Heisenberg model
Allès, B; Criado, C; Pepé, M
1999-01-01
We analyze the percolation properties of certain clusters defined on configurations of the 2--dimensional Heisenberg model thermalized at a temperature T=0.5. We find that, given any direction in O(3) space, \\vec{n}, the spins almost perpendicular to \\vec{n} form a percolating cluster. Given a fixed configuration, this is true for any \\vec{n}. We briefly comment on the critical properties of the model.
A fully coupled 2D model of equiaxed eutectic solidification
Charbon, Ch.; LeSar, R.
1995-12-31
We propose a model of equiaxed eutectic solidification that couples the macroscopic level of heat diffusion with the microscopic level of nucleation and growth of the eutectic grains. The heat equation with the source term corresponding to the latent heat release due to solidification is calculated numerically by means of an implicit finite difference method. In the time stepping scheme, the evolution of solid fraction is deduced from a stochastic model of nucleation and growth which uses the local temperature (interpolated from the FDM mesh) to determine the local grain density and the local growth rate. The solid-liquid interface of each grain is tracked by using a subdivision of each grain perimeter in a large number of sectors. The state of each sector (i.e. whether it is still in contact with the liquid or already captured by an other grain) and the increase of radius of each grain during one time step allows one to compute the increase of solid fraction. As for deterministic models, the results of the model are the evolution of temperature and of solid fraction at any point of the sample. Moreover the model provides a complete picture of the microstructure, thus not limiting the microstructural information to the average grain density but allowing one to compute any stereological value of interest. We apply the model to the solidification of gray cast iron.
Simulation of subgrid orographic precipitation with an embedded 2-D cloud-resolving model
Jung, Joon-Hee; Arakawa, Akio
2016-03-01
By explicitly resolving cloud-scale processes with embedded two-dimensional (2-D) cloud-resolving models (CRMs), superparameterized global atmospheric models have successfully simulated various atmospheric events over a wide range of time scales. Up to now, however, such models have not included the effects of topography on the CRM grid scale. We have used both 3-D and 2-D CRMs to simulate the effects of topography with prescribed "large-scale" winds. The 3-D CRM is used as a benchmark. The results show that the mean precipitation can be simulated reasonably well by using a 2-D representation of topography as long as the statistics of the topography such as the mean and standard deviation are closely represented. It is also shown that the use of a set of two perpendicular 2-D grids can significantly reduce the error due to a 2-D representation of topography.
Conservation laws and LETKF with 2D Shallow Water Model
Zeng, Yuefei; Janjic, Tijana
2016-04-01
Numerous approaches have been proposed to maintain physical conservation laws in the numerical weather prediction models. However, to achieve a reliable prediction, adequate initial conditions are also necessary, which are produced by a data assimilation algorithm. If an ensemble Kalman filters (EnKF) is used for this purpose, it has been shown that it could yield unphysical analysis ensemble that for example violates principles of mass conservation and positivity preservation (e.g. Janjic et al 2014) . In this presentation, we discuss the selection of conservation criteria for the analysis step, and start with testing the conservation of mass, energy and enstrophy. The simple experiments deal with nonlinear shallow water equations and simulated observations that are assimilated with LETKF (Localized Ensemble Transform Kalman Filter, Hunt et al. 2007). The model is discretized in a specific way to conserve mass, angular momentum, energy and enstrophy. The effects of the data assimilation on the conserved quantities (of mass, energy and enstrophy) depend on observation covarage, localization radius, observed variable and observation operator. Having in mind that Arakawa (1966) and Arakawa and Lamb (1977) showed that the conservation of both kinetic energy and enstrophy by momentum advection schemes in the case of nondivergent flow prevents systematic and unrealistic energy cascade towards high wave numbers, a cause of excessive numerical noise and possible eventual nonlinear instability, we test the effects on prediction depending on the type of errors in the initial condition. The performance with respect to nonlinear energy cascade is assessed as well.
Google Earth as a tool in 2-D hydrodynamic modeling
Chien, Nguyen Quang; Keat Tan, Soon
2011-01-01
A method for coupling virtual globes with geophysical hydrodynamic models is presented. Virtual globes such as Google TM Earth can be used as a visualization tool to help users create and enter input data. The authors discuss techniques for representing linear and areal geographical objects with KML (Keyhole Markup Language) files generated using computer codes (scripts). Although virtual globes offer very limited tools for data input, some data of categorical or vector type can be entered by users, and then transformed into inputs for the hydrodynamic program by using appropriate scripts. An application with the AnuGA hydrodynamic model was used as an illustration of the method. Firstly, users draw polygons on the Google Earth screen. These features are then saved in a KML file which is read using a script file written in the Lua programming language. After the hydrodynamic simulation has been performed, another script file is used to convert the resulting output text file to a KML file for visualization, where the depths of inundation are represented by the color of discrete point icons. The visualization of a wind speed vector field was also included as a supplementary example.
Point Contacts in Modeling Conducting 2D Planar Structures
Thiel, David V; Hettenhausen, Jan; Lewis, Andrew
2015-01-01
Use of an optimization algorithm to improve performance of antennas and electromagnetic structures usually ends up in planar unusual shapes. Using rectangular conducting elements the proposed structures sometimes have connections with only one single point in common between two neighboring areas. The single point connections (point crossing) can affect the electromagnetic performance of the structure. In this letter, we illustrate the influence of point crossing on dipole and loop antennas using MoM, FDTD, and FEM solvers. Current distribution, radiation pattern, and impedance properties for different junctions are different. These solvers do not agree in the modeling of the point crossing junctions which is a warning about uncertainty in using such junctions. However, solvers agree that a negligible change in the junction would significantly change the antenna performance. We propose that one should consider both bridging and chamfering of the conflicting cells to find optimized structures. This reduces the ...
Multiflavor bosonic Hubbard models in the first excited Bloch band of an optical lattice
We propose that by exciting ultracold atoms from the zeroth to the first Bloch band in an optical lattice, multiflavor bosonic Hubbard Hamiltonians can be realized in a different way. In these systems, each flavor hops in a separate direction and on-site exchange terms allow pairwise conversion between different flavors. Using band-structure calculations, we determine the parameters entering these Hamiltonians and derive the mean-field ground-state phase diagram for two effective Hamiltonians (two dimensional, two flavors, and three dimensional, three flavors). Further, we estimate the stability of atoms in the first band using second-order perturbation theory and find lifetimes that can be considerably (10-100 times) longer than the relevant time scale associated with intersite hopping dynamics, suggesting that quasiequilibrium can be achieved in these metastable states
2D modelling of polycrystalline silicon thin film solar cells
Leendertz Caspar
2013-07-01
Full Text Available The influence of grain boundary (GB properties on device parameters of polycrystalline silicon (poly-Si thin film solar cells is investigated by two-dimensional device simulation. A realistic poly-Si thin film model cell composed of antireflection layer, (n+-type emitter, thick p-type absorber, and (p+-type back surface field was created. The absorber consists of a low-defect crystalline Si grain with an adjacent highly defective grain boundary layer. The performances of a reference cell without GB, one with n-type and one with p-type GB, respectively, are compared. The doping concentration and defect density at the GB are varied. It is shown that the impact of the grain boundary on the poly-Si cell is twofold: a local potential barrier is created at the GB, and a part of the photogenerated current flows within the GB. Regarding the cell performance, a highly doped n-type GB is less critical in terms of the cell’s short circuit current than a highly doped p-type GB, but more detrimental in terms of the cell’s open circuit voltage and fill factor.
The electronic structure of the high-Tc copper oxides is calculated by means of an extended two-dimensional three-band Hubbard model in the unrestricted Hartree-Fock approximation. The influence of the coupling parameters on the obtained bands, as well as their doping dependence are investigated especially at the Fermi surface. Results are discussed in the light of recent experimental data for the cuprate Fermi surfaces. A comparative analysis of these conflicting data on the basis of our results sheds some light on the interpretation of the measured band structures. The direct oxygen-oxygen hopping interaction is found to be essential in fitting experimental results, suggesting that, in the doped regime, the oxygen band plays a key role at least in the near-EF region. Antiferromagnetic correlations among copper atoms turn out as well to be crucial. The results agree remarkably well with previous local-density calculations and with spectroscopic measurements
Phase boundary between spin singlet and triplet superconductivity in the extended Hubbard model with exchange interaction on a square lattice is calculated within meanfield approximation. Basically, antiferromagnetic exchange interaction J is advantageous for the singlet pairing, while ferromagnetic J prefers the triplet pairing. When off-site interaction V is repulsive, the singlet phase and the triplet phase are separated by normal state in the phase diagram against V and J. If V is effectively attractive, however, the singlet and triplet states can compete against each other. We calculate the phase boundary between singlet and triplet phase for various band filling. It is shown that the triplet phase penetrates rather deeply into antiferromagnetic exchange regime for lower band filling, whereas the penetration of the singlet phase is confined in a narrow range of ferromagnetic exchange regime.
We investigate the two-dimensional attractive Hubbard model with quantum Monte Carlo techniques to reveal the crossover from a BCS-type superconductivity in the weak-coupling regime to a superconductivity properly described by a Bose-Einstein condensation (BEC) of local, preformed pairs. The crossover from BCS to BEC is particularly well exposed in the temperature dependence of both the spin susceptibility and the double occupancy, as well as by the appearance of a pseudogap in the density of states far above Tc. These features are also mirrored in the shape of the specific-heat peak around Tc, the separation of the temperature regimes where pair formation and their condensation occur, and in the transfer of spectral weight from the single-particle excitation branch to a pair band in the normal state. copyright 1996 The American Physical Society
Phases and transitions in the spin-1 Bose-Hubbard model: Systematics of a mean-field theory
We generalize the mean-field theory for the spinless Bose-Hubbard model to account for the different types of superfluid phases that can arise in the spin-1 case. In particular, our mean-field theory can distinguish polar and ferromagnetic superfluids, Mott insulator, that arise at integer fillings at zero temperature, and normal Bose liquids into which the Mott insulators evolve at finite temperatures. We find, in contrast to the spinless case, that several of the superfluid-Mott insulator transitions are of first order at finite temperatures. Our systematic study yields rich phase diagrams that include first-order and second-order transitions and a variety of tricritical points. We discuss the possibility of realizing such phase diagrams in experimental systems
Momentum structure of the self-energy and its parametrization for the two-dimensional Hubbard model
Pudleiner, P.; Schäfer, T.; Rost, D.; Li, G.; Held, K.; Blümer, N.
2016-05-01
We compute the self-energy for the half-filled Hubbard model on a square lattice using lattice quantum Monte Carlo simulations and the dynamical vertex approximation. The self-energy is strongly momentum-dependent, but it can be parametrized via the noninteracting energy-momentum dispersion ɛk, except for pseudogap features right at the Fermi edge. That is, it can be written as Σ (ɛk,ω ) , with two energylike parameters (ɛ , ω ) instead of three (kx, ky, and ω ). The self-energy has two rather broad and weakly dispersing high-energy features and a sharp ω =ɛk feature at high temperatures, which turns to ω =-ɛk at low temperatures. Altogether this yields a Z - and reversed-Z -like structure, respectively, for the imaginary part of Σ (ɛk,ω ) . We attribute the change of the low-energy structure to antiferromagnetic spin fluctuations.