Plaquette expansion of the 2D anti-ferromagnetic Heisenberg model
The plaquette expansion of the Lanczos recursion method is applied to the two dimensional anti-ferromagnetic Heisenberg model. Connected Hamiltonian moments are calculated with respect to the Neel state up to n = 6. The subsequent plaquette expansion of the Lanczos matrix in the number of plaquettes on the lattice, Np, is determined to order 1/Np. Diagonalizing the Lanczos matrix in this form gives an upper bound on the energy density of -0.664 in the limit Np → ∞, in good agreement with existing calculations. 4 refs., 1 tab., 2 figs
Excitation of bond-alternating spin-1/2 Heisenberg chains by tunnelling electrons
Inelastic electron tunneling spectra (IETS) are evaluated for spin-1/2 Heisenberg chains showing different phases of their spin ordering. The spin ordering is controlled by the value of the two different Heisenberg couplings on the two sides of each of the chain's atoms (bond-alternating chains). The perfect anti-ferromagnetic phase, i.e. a unique exchange coupling, marks a topological quantum phase transition (TQPT) of the bond-alternating chain. Our calculations show that the TQPT is recognizable in the excited states of the chain and hence that IETS is in principle capable of discriminating the phases. We show that perfectly symmetric chains, such as closed rings mimicking infinite chains, yield the same spectra on both sides of the TQPT and IETS cannot reveal the nature of the spin phase. However, for finite size open chains, both sides of the TQPT are associated with different IETS spectra, especially on the edge atoms, thus outlining the transition. (paper)
Seeing time-reversal transmission characteristics through kinetic anti-ferromagnetic Ising chain
Chen Ying-Ming; Wang Bing-Zhong
2012-01-01
As an example of our new approach to complex near-field (NF) scattering of electromagnetic waves,the timereversal (TR) transmission process on an NF current-element array is mapped to the statistical process on a kinetic Ising transmission chain.Equilibrium statistical mechanics and non-equilibrium Monte Carlo (MC) dynamics help us to find signal jamming,aging,annihilating,creating,and TR symmetry breaking on the chain with inevitable background noises; and these results are general in NF systems where complex electromagnetic scattering arises.
Seeing time-reversal transmission characteristics through kinetic anti-ferromagnetic Ising chain
As an example of our new approach to complex near-field (NF) scattering of electromagnetic waves, the time-reversal (TR) transmission process on an NF current-element array is mapped to the statistical process on a kinetic Ising transmission chain. Equilibrium statistical mechanics and non-equilibrium Monte Carlo (MC) dynamics help us to find signal jamming, aging, annihilating, creating, and TR symmetry breaking on the chain with inevitable background noises; and these results are general in NF systems where complex electromagnetic scattering arises. (condensed matter: structural, mechanical, and thermal properties)
Edge states in Open Antiferromagnetic Heisenberg Chains
Qin, Shaojin; Ng, Tai-Kai; Su, Zhao-Bin
1995-01-01
In this letter we report our results in investigating edge effects of open antiferromagnetic Heisenberg spin chains with spin magnitudes $S=1/2, 1,3/2,2$ using the density-matrix renormalization group (DMRG) method initiated by White. For integer spin chains, we find that edge states with spin magnitude $S_{edge}=S/2$ exist, in agreement with Valence-Bond-Solid model picture. For half-integer spin chains, we find that no edge states exist for $S=1/2$ spin chain, but edge state exists in $S=3/...
Magnetic Heisenberg-chain/pp-wave correspondence
We find a decoupling limit of planar N = 4 super Yang-Mills (SYM) on R x S3 in which it becomes equivalent to the ferromagnetic XXX1/2 Heisenberg spin chain in an external magnetic field. The decoupling limit generalizes the one found in ref. [4] corresponding to the case with zero magnetic field. The presence of the magnetic field is seen to break the degeneracy of the vacuum sector and it has a non-trivial effect on the low energy spectrum. We find a general connection between the Hagedorn temperature of planar N = 4 SYM on R x S3 in the decoupling limit and the thermodynamics of the Heisenberg chain. This is used to study the Hagedorn temperature for small and large value of the effective coupling. We consider the dual decoupling limit of type IIB strings on AdS5 x S5. We find a Penrose limit compatible with the decoupling limit that gives a magnetic pp-wave background. The breaking of the symmetry by the magnetic field on the gauge theory side is seen to have a geometric counterpart in the derivation of the Penrose limit. We take the decoupling limit of the pp-wave spectrum and succesfully match the resulting spectrum to the low energy spectrum on the gauge theory side. This enables us to match the Hagedorn temperature of the pp-wave to the Hagedorn temperature of the gauge theory for large effective coupling. This generalizes the results of ref. [5] to the case of non-zero magnetic field
Ising and Heisenberg models on ferrimagnetic AB sub 2 chains
Vitoriano, C; Raposo, E P
2002-01-01
We study the Ising and Heisenberg models on one-dimensional ferrimagnetic bipartite chains with the special AB sub 2 unit-cell topology and experimental motivation in inorganic and organic magnetic polymers. The spin-1/2 AB sub 2 Ising case is exactly solved in the presence of an external magnetic field. We also derive asymptotical low- and high-temperature limits of several thermodynamical quantities of the zero-field classical AB sub 2 Heisenberg model. Further, the quantum spin-1/2 AB sub 2 Heisenberg model in a field is studied using a mean-field approach.
The spin-partitioned total position-spread tensor: An application to Heisenberg spin chains
The spin partition of the Total Position-Spread (TPS) tensor has been performed for one-dimensional Heisenberg chains with open boundary conditions. Both the cases of a ferromagnetic (high-spin) and an anti-ferromagnetic (low-spin) ground-state have been considered. In the case of a low-spin ground-state, the use of alternating magnetic couplings allowed to investigate the effect of spin-pairing. The behavior of the spin-partitioned TPS (SP-TPS) tensor as a function of the number of sites turned to be closely related to the presence of an energy gap between the ground-state and the first excited-state at the thermodynamic limit. Indeed, a gapped energy spectrum is associated to a linear growth of the SP-TPS tensor with the number of sites. On the other hand, in gapless situations, the spread presents a faster-than-linear growth, resulting in the divergence of its per-site value. Finally, for the case of a high-spin wave function, an analytical expression of the dependence of the SP-TPS on the number of sites n and the total spin-projection Sz has been derived
The spin-partitioned total position-spread tensor: An application to Heisenberg spin chains
Fertitta, Edoardo; Paulus, Beate [Institut für Chemie und Biochemie, Freie Universität Berlin, Takustr. 3, 14195 Berlin (Germany); El Khatib, Muammar; Evangelisti, Stefano; Leininger, Thierry [Laboratoire de Chimie et Physique Quantiques–LCPQ/IRSAMC, Université de Toulouse (UPS) et CNRS (UMR-5626), 118 Route de Narbonne, Toulouse Cedex 31062 (France); Bendazzoli, Gian Luigi [Dipartimento di Chimica Industriale “Toso Montanari,” Università di Bologna, Viale Risorgimento 4, I–40136 Bologna (Italy)
2015-12-28
The spin partition of the Total Position-Spread (TPS) tensor has been performed for one-dimensional Heisenberg chains with open boundary conditions. Both the cases of a ferromagnetic (high-spin) and an anti-ferromagnetic (low-spin) ground-state have been considered. In the case of a low-spin ground-state, the use of alternating magnetic couplings allowed to investigate the effect of spin-pairing. The behavior of the spin-partitioned TPS (SP-TPS) tensor as a function of the number of sites turned to be closely related to the presence of an energy gap between the ground-state and the first excited-state at the thermodynamic limit. Indeed, a gapped energy spectrum is associated to a linear growth of the SP-TPS tensor with the number of sites. On the other hand, in gapless situations, the spread presents a faster-than-linear growth, resulting in the divergence of its per-site value. Finally, for the case of a high-spin wave function, an analytical expression of the dependence of the SP-TPS on the number of sites n and the total spin-projection S{sub z} has been derived.
Low temperature spin wave dynamics in classical Heisenberg chains
Heller, P.; Blume, M.
1977-11-01
A detailed and quantitative study of the low-temperature spin-wave dynamics was made for the classical Heisenberg-coupled chain using computer simulation. Results for the spin-wave damping rates and the renormalization of the spin-wave frequencies are presented and compared with existing predictions.
Phonon dynamics in a compressible classical Heisenberg chain
Fivez, Jan; Raedt, Hans De; Raedt, Bart De
1980-01-01
The dynamic properties of the compressible classical Heisenberg chain with bilinear coupling are investigated. The sound velocity is calculated exactly. The Fourier-transformed displacement-displacement correlation function is studied as a function of temperature, wave vector, and the model paramete
Teleportation via thermally entangled states of a two-qubit Heisenberg XXZ chain
QIN Meng; TAO Ying-Juan; TIAN Dong-Ping
2008-01-01
We investigate quantum teleportation as a tool to study the thermally entangled state of a twoqubit Heisenberg XXZ chain.Our work is mainly to investigate the characteristics of a Heisenberg XXZ chain and get some analytical results of the fully entangled fraction.We also consider the entanglement teleportation via a two-qubit Heisenberg XXZ chain.
The Heisenberg XX spin chain and low-energy QCD
Pérez-García, David; Tierz, Miguel
2013-01-01
By using random matrix models we uncover a connection between the low energy sector of four dimensional QCD at finite volume and the Heisenberg XX model in a 1d spin chain. This connection allows to relate crucial properties of QCD with physically meaningful properties of the spin chain, establishing a dictionary between both worlds. We predict for the spin chain a third-order phase transition and a Tracy-Widom law in the transition region. We postulate that this dictionary goes beyond the pa...
Quantum Correlations and Teleportation in Heisenberg XX Spin Chain
Qin, Wan; Guo, Jin-Liang
2015-07-01
We investigate the thermal quantum correlations in the Heisenberg XX spin chain, and the teleportation of a two-qubit entangled state via the spin chain is analyzed. It is found that the effects of external magnetic field and three-site interaction on the thermal entanglement and quantum discord between the nearest or the next nearest neighbor qubits behave differently in various aspects. Special attention is paid to how to enhance the quantum correlations of the output state and the average fidelity of the teleportation. We find that quantum discord gives a better performance in the quantum correlations transmission, and the three-site interaction is necessary for a successful teleportation.
Spin transport of weakly disordered Heisenberg chain at infinite temperature
Khait, Ilia; Gazit, Snir; Yao, Norman Y.; Auerbach, Assa
2016-06-01
We study the disordered Heisenberg spin chain, which exhibits many-body localization at strong disorder, in the weak to moderate disorder regime. A continued fraction calculation of dynamical correlations is devised, using a variational extrapolation of recurrents. Good convergence for the infinite chain limit is shown. We find that the local spin correlations decay at long times as C ˜t-β , whereas the conductivity exhibits a low-frequency power law σ ˜ωα . The exponents depict subdiffusive behavior β 0 at all finite disorders and convergence to the scaling result α +2 β =1 at large disorders.
Quasiparticle interactions in frustrated Heisenberg chains
Vanderstraeten, Laurens; Haegeman, Jutho; Verstraete, Frank; Poilblanc, Didier
2016-06-01
Interactions between elementary excitations in quasi-one-dimensional antiferromagnets are of experimental relevance and their quantitative theoretical treatment has been a theoretical challenge for many years. Using matrix product states, one can explicitly determine the wave functions of the one- and two-particle excitations, and, consequently, the contributions to dynamical correlations. We apply this framework to the (nonintegrable) frustrated dimerized spin-1/2 chain, a model for generic spin-Peierls systems, where low-energy quasiparticle excitations are bound states of topological solitons. The spin structure factor involving two quasiparticle scattering states is obtained in the thermodynamic limit with full momentum and frequency resolution. This allows very subtle features in the two-particle spectral function to be revealed which, we argue, could be seen, e.g., in inelastic neutron scattering of spin-Peierls compounds under a change of the external pressure.
Entanglement Perturbation Theory for Antiferromagnetic Heisenberg Spin Chains
Wang, Lihua; Chung, Sung Gong
2012-11-01
A recently developed numerical method, entanglement perturbation theory (EPT), is used to study the antiferromagnetic Heisenberg spin chains with z-axis anisotropy λ and magnetic field B. To demonstrate its accuracy, we first apply EPT to the isotropic spin-1/2 antiferromagnetic Heisenberg model, and find that EPT successfully reproduces the exact Bethe ansatz results for the ground state energy, the local magnetization, and the spin correlation functions (Bethe ansatz result is available for the first seven lattice separations). In particular, EPT confirms for the first time the asymptotic behavior of the spin correlation functions predicted by the conformal field theory, which realizes only for lattice separations larger than 1000. Next, turning on the z-axis anisotropy and the magnetic field, the 2- and 4-spin correlation functions are calculated, and the results are compared with those obtained by bosonization and density matrix renormalization group methods. Finally, for the spin-1 antiferromagnetic Heisenberg model, the ground state phase diagram in λ space is determined by Roomany--Wyld renormalization group (RG) finite size scaling. The results are in good agreement with those obtained by the level-spectroscopy method.
Quantum Teleportation Through a Two-Qubit Heisenberg XXZ Chain
We consider a two-qubit Heisenberg XXZ chain as a resource for quantum teleportation via the standard teleportation protocol T0. The effects of anisotropic on teleportation fidelity and entanglement are studied in detail. We find anisotropic not only improves the critical temperature Tc and critical magnetic field Bc, beyond which quantum teleportation is inferior to classical communication protocol, but also enhances the fidelity for fixed magnetic field B and temperature T. For entanglement teleportation, the effects of magnetic field on average fidelity and output entanglement are studied
Q-operators for the open Heisenberg spin chain
Rouven Frassek
2015-12-01
Full Text Available We construct Q-operators for the open spin-12 XXX Heisenberg spin chain with diagonal boundary matrices. The Q-operators are defined as traces over an infinite-dimensional auxiliary space involving novel types of reflection operators derived from the boundary Yang–Baxter equation. We argue that the Q-operators defined in this way are polynomials in the spectral parameter and show that they commute with transfer matrix. Finally, we prove that the Q-operators satisfy Baxter's TQ-equation and derive the explicit form of their eigenvalues in terms of the Bethe roots.
Q-operators for the open Heisenberg spin chain
Frassek, Rouven; Szécsényi, István M.
2015-12-01
We construct Q-operators for the open spin-1/2 XXX Heisenberg spin chain with diagonal boundary matrices. The Q-operators are defined as traces over an infinite-dimensional auxiliary space involving novel types of reflection operators derived from the boundary Yang-Baxter equation. We argue that the Q-operators defined in this way are polynomials in the spectral parameter and show that they commute with transfer matrix. Finally, we prove that the Q-operators satisfy Baxter's TQ-equation and derive the explicit form of their eigenvalues in terms of the Bethe roots.
Q-operators for the open Heisenberg spin chain
Frassek, Rouven
2015-01-01
We construct Q-operators for the open spin-1/2 XXX Heisenberg spin chain with diagonal boundary matrices. The Q-operators are defined as traces over an infinite-dimensional auxiliary space involving novel types of reflection operators derived from the boundary Yang-Baxter equation. We argue that the Q-operators defined in this way are polynomials in the spectral parameter and show that they commute with transfer matrix. Finally, we prove that the Q-operators satisfy Baxter's TQ-equation.
Stochastic motion of solitary excitations on the classical Heisenberg chain
We study stochastic motion of solitary excitations on a classical, discrete, isotropic, ferromagnetic Heisenberg spin chain with nearest-neighbour exchange interactions. Gaussian white noise is coupled to the spins in a way that allows for the noise to be interpreted as a stochastic magnetic field. The noise translates into a collective stochastic force affecting a solitary excitation as a whole. The position of a solitary excitation has to be calculated from the noisy spin configuration, i.e. the position is defined as a function of the spin components. Two examples of such definitions are given, because we want to investigate the dependence of the results on the choice of definition. Using these definitions, we calculate the variance of the position as a function of time and determine the variance from simulations as well. The calculations require knowledge of the shape of the solitary wave. We approximate the shape with that of soliton solutions of the continuum Heisenberg chain, restricting our considerations to solitary waves of large width, in which case this approximation is good. The calculations yield a linear dependence of the variance on time, the slope being determined by parameters describing the shape of the soliton. The two definitions of the position we use provide different results for this slope. The origin of this difference is discussed. With both definitions very good agreement is found between the results of the simulations and the corresponding theoretical results, for not too large time scales. (author)
Quantum communication through anisotropic Heisenberg XY spin chains
We study quantum communication through an anisotropic Heisenberg XY chain in a transverse magnetic field. We find that for some time t and anisotropy parameter γ, one can transfer a state with a relatively high fidelity. In the strong-field regime, the anisotropy does not significantly affect the fidelity while in the weak-field regime the affect is quite pronounced. The most interesting case is the intermediate regime where the oscillation of the fidelity with time is low and the high-fidelity peaks are relatively broad. This would, in principle, allow for quantum communication in realistic circumstances. Moreover, we calculate the purity, or tangle, as a measure of the entanglement between one spin and all the other spins in the chain and find that the stronger the anisotropy and exchange interaction, the more entanglement will be generated for a given time
Overlap distributions for quantum quenches in the anisotropic Heisenberg chain
Mazza, Paolo P.; Stéphan, Jean-Marie; Canovi, Elena; Alba, Vincenzo; Brockmann, Michael; Haque, Masudul
2016-01-01
The dynamics after a quantum quench is determined by the weights of the initial state in the eigenspectrum of the final Hamiltonian, i.e. by the distribution of overlaps in the energy spectrum. We present an analysis of such overlap distributions for quenches of the anisotropy parameter in the one-dimensional anisotropic spin-1/2 Heisenberg model (XXZ chain). We provide an overview of the form of the overlap distribution for quenches from various initial anisotropies to various final ones, using numerical exact diagonalization. We show that if the system is prepared in the antiferromagnetic Néel state (infinite anisotropy) and released into a non-interacting setup (zero anisotropy, XX point) only a small fraction of the final eigenstates gives contributions to the post-quench dynamics, and that these eigenstates have identical overlap magnitudes. We derive expressions for the overlaps, and present the selection rules that determine the final eigenstates having nonzero overlap. We use these results to derive concise expressions for time-dependent quantities (Loschmidt echo, longitudinal and transverse correlators) after the quench. We use perturbative analyses to understand the overlap distribution for quenches from infinite to small nonzero anisotropies, and for quenches from large to zero anisotropy.
The generalized Gibbs ensemble for Heisenberg spin chains
We consider the generalized Gibbs ensemble (GGE) in the context of global quantum quenches in XXZ Heisenberg spin chains. Embedding the GGE into the quantum transfer matrix formalism, we develop an iterative procedure to fix the Lagrange multipliers and to calculate predictions for the long-time limit of short-range correlators. The main idea is to consider truncated GGEs with only a finite number of charges and to investigate the convergence of the numerical results as the truncation level is increased. As an example we consider a quantum quench situation where the system is initially prepared in the Néel state and then evolves with an XXZ Hamiltonian with anisotropy Δ > 1. We provide predictions for short-range correlators and gather numerical evidence that the iterative procedure indeed converges. The results show that the system retains memory of the initial condition, and there are clear differences between the numerical values of the correlators as calculated from the purely thermal and generalized Gibbs ensembles. (paper)
Abgaryan, V S; Ananikian, N. S.; Ananikyan, L. N.; Hovhannisyan, V.
2014-01-01
Thermal entanglement, magnetic and quadrupole moments properties of the mixed spin-1/2 and spin-1 Ising-Heisenberg model on a diamond chain are considered. Magnetization and quadrupole moment plateaus are observed for the antiferromagnetic couplings. Thermal negativity as a measure of quantum entanglement of the mixed spin system is calculated. Different behavior for the negativity is obtained for the various values of Heisenberg dipolar and quadrupole couplings. The intermediate plateau of t...
Strong Coulomb effects in hole-doped Heisenberg chains
Schnack, J.
2005-06-01
Substances such as the “telephone number compound” Sr14Cu24O41 are intrinsically hole-doped. The involved interplay of spin and charge dynamics is a challenge for theory. In this article we propose to describe hole-doped Heisenberg spin rings by means of complete numerical diagonalization of a Heisenberg Hamiltonian that depends parametrically on hole positions and includes the screened Coulomb interaction among the holes. It is demonstrated that key observables like magnetic susceptibility, specific heat, and inelastic neutron scattering cross section depend sensitively on the dielectric constant of the screened Coulomb potential.
Determinant representation for the time dependent correlation functions in the XX0 Heisenberg chain
Time dependent correlation functions in the Heisenberg XX0 chain in the external transverse magnetic field are calculated. For a finite chain normalized mean values of local spin products are represented as determinants of NxN matrices, N being the number of quasiparticles in the corresponding eigenstate of the Hamiltonian. In the thermodynamical limit (infinitely long chain), correlation functions are expressed in terms of Fredholm determinants of linear integral operators. (author) 24 refs
Thermal entanglement in a two-qubit Heisenberg XY chain with the Dzyaloshinskii-Moriya interaction
Qin Meng; Xu Sheng-Long; Tao Ying-Juan; Tian Dong-Ping
2008-01-01
This paper investigates thermal entanglements of a two-qubit Heisenberg XY chain in the presence of the Dzyaioshinskii-Moriya anisotropic antisymmetric interaction. By the concept of concurrence, it is found that the effects of spin-orbit coupling on the entanglement are different from those of spin-spin model. The analytical expressions of concurrence are obtained for this model.
Abgaryan, V. S.; Ananikian, N. S.; Ananikyan, L. N.; Hovhannisyan, V.
2015-02-01
Thermal entanglement, magnetic and quadrupole moments properties of the mixed spin-1/2 and spin-1 Ising-Heisenberg model on a diamond chain are considered. Magnetization and quadrupole moment plateaus are observed for the antiferromagnetic couplings. Thermal negativity as a measure of quantum entanglement of the mixed spin system is calculated. Different behavior for the negativity is obtained for the various values of Heisenberg dipolar and quadrupole couplings. The intermediate plateau of the negativity has been observed at the absence of the single-ion anisotropy and quadrupole interaction term. When dipolar and quadrupole couplings are equal there is a similar behavior of negativity and quadrupole moment.
Ground state properties of a spin chain within Heisenberg model with a single lacking spin site
MEBROUKI, M.
2011-01-01
The ground state and first excited state energies of an antiferromagnetic spin-1/2 chain with and without a single lacking spin site are computed using exact diagonalization method, within the Heisenberg model. In order to keep both parts of a spin chain with a lacking site connected, next nearest neighbors interactions are then introduced. Also, the Density Matrix Renormalization Group (DMRG) method is used, to investigate ground state energies of large system sizes; which permits us to inq...
Topological basis realization for BMW algebra and Heisenberg XXZ spin chain model
Liu, Bo; Xue, Kang; Wang, Gangcheng; Liu, Ying; Sun, Chunfang
2015-04-01
In this paper, we study three-dimensional (3D) reduced Birman-Murakami-Wenzl (BMW) algebra based on topological basis theory. Several examples of BMW algebra representations are reviewed. We also discuss a special solution of BMW algebra, which can be used to construct Heisenberg XXZ model. The theory of topological basis provides a useful method to solve quantum spin chain models. It is also shown that the ground state of XXZ spin chain is superposition state of topological basis.
Antiferromagnetic Heisenberg Spin Chain of a Few Cold Atoms in a One-Dimensional Trap
Murmann, S.; Deuretzbacher, F.; Zürn, G.; Bjerlin, J.; Reimann, S. M.; Santos, L.; Lompe, T.; Jochim, S.
2015-11-01
We report on the deterministic preparation of antiferromagnetic Heisenberg spin chains consisting of up to four fermionic atoms in a one-dimensional trap. These chains are stabilized by strong repulsive interactions between the two spin components without the need for an external periodic potential. We independently characterize the spin configuration of the chains by measuring the spin orientation of the outermost particle in the trap and by projecting the spatial wave function of one spin component on single-particle trap levels. Our results are in good agreement with a spin-chain model for fermionized particles and with numerically exact diagonalizations of the full few-fermion system.
Finite size scaling for low energy excitations in integer Heisenberg spin chains
In this paper we study the finite size scaling for low energy excitations of S = 1 and S = 2 Heisenberg chains, using the density matrix renormalization group technique. A crossover from 1/L behaviour (with L as the chain length) for medium chain length to 1/L2 scaling for long chain length is found for excitations in the continuum band as the length of the open chain increases. Topological spin S = 1/2 excitations are shown to give rise to the two lowest energy states for both open and periodic S = 1 chains. In periodic chains these two excitations are ''confined'' next to each other, while for open chains they are two free edge 1/2 spins. The finite size scaling of the two lowest energy excitations of open S = 2 chains is determined by coupling the two free edge S = 1 spins. The gap and correlation length for S = 2 open Heisenberg chains are shown to be 0.082 (in units of the exchange J) and 47, respectively. (author). 23 refs, 5 figs
A quaternionic map for the steady states of the Heisenberg spin-chain
We show that the steady states of the classical Heisenberg XXX spin-chain in an external magnetic field can be found by iterations of a quaternionic map. A restricted model, e.g., the xy spin-chain is known to have spatially chaotic steady states and the phase space occupied by these chaotic states is known to go through discrete changes as the field strength is varied. The same phenomenon is studied for the xxx spin-chain. It is seen that in this model the phase space volume varies smoothly with the external field.
A quaternionic map for the steady states of the Heisenberg spin-chain
Mehta, Mitaxi P., E-mail: mitaxi.mehta@ahduni.edu.in [IICT, Ahmedabad University, Opp. IIM, Navrangpura, Ahmedabad (India); Dutta, Souvik; Tiwari, Shubhanshu [BITS-Pilani, K.K. Birla Goa campus, Goa (India)
2014-01-17
We show that the steady states of the classical Heisenberg XXX spin-chain in an external magnetic field can be found by iterations of a quaternionic map. A restricted model, e.g., the xy spin-chain is known to have spatially chaotic steady states and the phase space occupied by these chaotic states is known to go through discrete changes as the field strength is varied. The same phenomenon is studied for the xxx spin-chain. It is seen that in this model the phase space volume varies smoothly with the external field.
Mapping between the Heisenberg XX Spin Chain and Low-Energy QCD
Pérez-García, David; Tierz, Miguel
2014-04-01
By using random matrix models, we uncover a connection between the low-energy sector of four-dimensional QCD at finite volume and the Heisenberg XX model in a 1D spin chain. This connection allows us to relate crucial properties of QCD with physically meaningful properties of the spin chain, establishing a dictionary between both worlds. For the spin chain, we predict a third-order phase transition and a Tracy-Widom law in the transition region. We also comment on possible numerical implications of the connection as well as on possible experimental implementations.
Mapping between the Heisenberg XX Spin Chain and Low-Energy QCD
Pérez García, David; Tierz, Miguel
2014-01-01
By using random matrix models, we uncover a connection between the low-energy sector of four-dimensional QCD at finite volume and the Heisenberg XX model in a 1D spin chain. This connection allows us to relate crucial properties of QCD with physically meaningful properties of the spin chain, establishing a dictionary between both worlds. For the spin chain, we predict a third-order phase transition and a Tracy-Widom law in the transition region. We also comment on possible numerical implicati...
Frustrated diamond-chain quantum XXZ Heisenberg antiferromagnet in a magnetic field
We consider the antiferromagnetic spin-1/2 XXZ Heisenberg model on a frustrated diamond-chain lattice in a z- or x-aligned external magnetic field. We use the strong-coupling approach to elaborate an effective description in the low-temperature strong-field regime. The obtained effective models are spin-1/2 XY chains which are exactly solvable through the Jordan–Wigner fermionization. We perform exact-diagonalization studies of the magnetization curves to test the quality of the effective description. The results may have relevance for the description of the azurite spin-chain compound
Algebraic Bethe ansatz for Q-operators: the Heisenberg spin chain
Frassek, Rouven
2015-07-01
We diagonalize Q-operators for rational homogeneous {sl}(2)-invariant Heisenberg spin chains using the algebraic Bethe ansatz. After deriving the fundamental commutation relations relevant for this case from the Yang-Baxter equation we demonstrate that the Q-operators act diagonally on the Bethe vectors if the Bethe equations are satisfied. In this way we provide a direct proof that the eigenvalues of the Q-operators studied here are given by Baxter's Q-functions.
Temperature Dependence of Energy Gaps in Spin-1/2 Dimerized Heisenberg Chain
江学范; 邢定钰; 陈鸿
2002-01-01
We present a method which combines a thermal coherent state approach with a self-consistent quantum theory to investigate the spin-1/2 dimerized antiferromagnetic Heisenberg chain. It is found that both excitation gaps between the ground state and two lowest excited modes, the triplet one-magnon excitation and the singlet twomagnon bound state decrease monotonically with increasing temperature. Our results are consistent with those obtained from the other approximations.
Quantum teleportation via a two-qubit Heisenberg XY chain-effects of anisotropy and magnetic field
In this paper we study the influence of anisotropy on the usefulness of the entanglement in a two-qubit Heisenberg XY chain at thermal equilibrium in the presence of an external magnetic field, as a resource for quantum teleportation via the standard teleportation protocol. We show that the nonzero thermal entanglement produced by adjusting the external magnetic field beyond some critical strength is a useful resource. We also consider entanglement teleportation via two two-qubit Heisenberg XY chains
Thermal entanglement of the Ising-Heisenberg diamond chain with Dzyaloshinskii-Moriya interaction
Qiao, Jie; Zhou, Bin
2015-11-01
We investigate the thermal entanglement in a spin-1/2 Ising-Heisenberg diamond chain, in which the vertical Heisenberg spin dimers alternate with single Ising spins. Due to the fact that the Dzyaloshinskii-Moriya (DM) interaction contributes to unusual and interesting magnetic properties in actual materials, and moreover it plays a significant role in the degree of the entanglement of the Heisenberg quantum spin systems, we focus on the effects of different DM interactions, including Dz and Dx, on the thermal entanglement of the Heisenberg spin dimer. The concurrence, as a measure of spin dimer entanglement, is calculated for different values of exchange interactions, DM interaction, external magnetic field, and temperature. It is found that the critical temperature and the critical magnetic field corresponding to the vanishing of entanglement increase with DM interaction, and the entanglement revival region gets larger by increasing DM interaction, thus DM interaction favors the formation of the thermal entanglement. It is observed that different DM interaction parameters (Dz and Dx) have remarkably different influences on the entanglement. Different from the case Dz, there is the non-monotonic variation of the concurrence with temperature in the case Dx, and additionally the DM interaction Dx can induce the entanglement near zero temperature in the case that the antiferromagnetic Ising-type interaction constant is larger than the antiferromagnetic Heisenberg interaction constant. It is also shown that for the same value of DM interaction the critical magnetic field of the case Dx is larger than that of the case Dz. Project supported by the National Natural Science Foundation of China (Grant No. 11274102), the New Century Excellent Talents in University of Ministry of Education of China (Grant No. NCET-11-0960), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20134208110001).
Quantum entanglement in trimer spin-1/2 Heisenberg chains with antiferromagnetic coupling
Del Cima, O M; da Silva, S L L
2015-01-01
The quantum entanglement measure is determined, for the first time, for antiferromagnetic trimer spin-1/2 Heisenberg chains. The physical quantity proposed to measure the entanglement is the distance between states by adopting the Hilbert-Schmidt norm. The method is applied to the new magnetic Cu(II) trimer system, 2b.3CuCl_2.2H_2O, and to the trinuclear Cu(II) halide salt, (3MAP)_2Cu_2Cl_8. The decoherence temperature, above which the entanglement is suppressed, is determined for the both systems. A correlation among their decoherence temperatures and their respective exchange coupling constants is established.
Quantum lattice fluctuations in a frustrated Heisenberg spin-Peierls chain
Weisse, A.; Wellein, G.; Fehske, H.
1999-01-01
As a simple model for spin-Peierls systems we study a frustrated Heisenberg chain coupled to optical phonons. In view of the anorganic spin-Peierls compound CuGeO3 we consider two different mechanisms of spin-phonon coupling. Combining variational concepts in the adiabatic regime and perturbation theory in the anti-adiabatic regime we derive effective spin Hamiltonians which cover the dynamical effect of phonons in an approximate way. Ground-state phase diagrams of these models are determined...
We studied the trace distance, the Hellinger distance, and the Bures distance geometric quantum discords (GQDs) for a two-spin Heisenberg XX chain with the Dzyaloshinsky–Moriya (DM) interaction and the external magnetic fields. We found that considerable enhancement of the GQDs can be achieved by introducing the DM interaction, and their maxima were obtained when the strength of the DM interaction approaches infinity. The external magnetic fields and the increase of the temperature can also enhance the GQDs to some extent during certain specific parameter regions
Quantum phase transition and entanglement in Heisenberg XX spin chain with impurity
In this paper, we study the quantum phase transition and the effect of impurity on the thermal entanglement between any two lattices in three-qubit Heisenberg XX chain in a uniform magnetic field. We show that the quantum phase transition always appears when impurity parameter is an arbitrary constant and unequal to zero, the external magnetic field and impurity parameters have a great effect on it. Also, there exists a relation between the quantum phase transition and the entanglement. By modulating the temperature, magnetic field and the impurity parameters, the entanglement between any two lattices can exhibit platform-like behaviour, which can be used to realize entanglement switch. (general)
Disorder-induced phases in the S=1 antiferromagnetic Heisenberg chain
Lajkó, Péter; Carlon, Enrico; Rieger, Heiko; Iglói, Ferenc
2005-09-01
We use extensive density matrix renormalization group (DMRG) calculations to explore the phase diagram of the random S=1 antiferromagnetic Heisenberg chain with a power-law distribution of the exchange couplings. We use open chains and monitor the lowest gaps, the end-to-end correlation function and the string order parameter. For this distribution at weak disorder, the system is in the gapless Haldane phase with a disorder dependent dynamical exponent, z , and z=1 signals the border between the nonsingular and singular regions of the local susceptibility. For strong enough disorder, which approximately corresponds to a uniform distribution, a transition into the random singlet phase is detected, at which the string order parameter as well as the average end-to-end correlation function are vanishing and at the same time the dynamical exponent is divergent. Singularities of physical quantities are found to be somewhat different in the random singlet phase and in the critical point.
Quantum Teleportation via Completely Anisotropic Heisenberg Chain in Inhomogeneous Magnetic Field
The quantum teleportation with the entangled thermal state is investigated based on the completely anisotropic Heisenberg chain in the presence of the externally inhomogeneous magnetic field. The effects of the anisotropy and magnetic field for the quantum fidelity are studied in detail. The zero temperature limit and the features of the nonzero temperature for this nonclassical fidelity are obtained. We find that the quantum teleportation demands more stringent conditions than the thermal entanglement of the resource by investigating the threshold temperature of the thermal concurrence and the critical temperature of the maximal teleportation fidelity. The useful quantum teleportation should avoid the point of the phase transition of the system and the anisotropy of the chain and the external magnetic field can control the applicability of the resource in the quantum teleportation. (general)
Thermal entanglement of a two-qubit Heisenberg chain in the presence of the Dzyaloshinski-Moriya (DM) anisotropic antisymmetric interaction and entanglement teleportation when using two independent Heisenberg chains as the quantum channel are investigated. It is found that the DM interaction can excite entanglement and teleportation fidelity. The output entanglement increases linearly with increasing value of the input; its dependences on the temperature, DM interaction, and spin coupling constant are given in detail. Entanglement teleportation will be better realized via an antiferromagnetic spin chain when the DM interaction is turned off and the temperature is low. However, the introduction of the DM interaction can cause the ferromagnetic spin chain to be a better quantum channel for teleportation. A minimal entanglement of the thermal state in the model is needed to realize the entanglement teleportation regardless of whether the spin chains are antiferromagnetic or ferromagnetic
Lari, Behzad
2011-01-01
This is a thesis submitted to university of Pune, India, for the Ph.D. degree. This work deals with entanglement production in two qubit, two qutrit and three qubit systems, entanglement in indistinguishable fermionic systems, quantum discord in a Heisenberg chain and geometric measure of quantum discord in an arbitrary state of a bipartite quantum system.
Quantum lattice fluctuations in a frustrated Heisenberg spin-Peierls chain
Weiße, A.; Wellein, G.; Fehske, H.
1999-09-01
As a simple model for spin-Peierls systems we study a frustrated Heisenberg chain coupled to optical phonons. In view of the anorganic spin-Peierls compound CuGeO3 we consider two different mechanisms of spin-phonon coupling. Combining variational concepts in the adiabatic regime and perturbation theory in the antiadiabatic regime we derive effective spin Hamiltonians which cover the dynamical effect of phonons in an approximate way. Ground-state phase diagrams of these models are determined, and the effect of frustration is discussed. Comparing the properties of the ground state and low-lying excitations with exact diagonalization data for the full quantum spin-phonon models, good agreement is found especially in the antiadiabatic regime.
Correlation functions of XX0 Heisenberg chain, q-binomial determinants, and random walks
Bogoliubov, N.M.; Malyshev, C.
2014-02-15
The XX0 Heisenberg model on a cyclic chain is considered. The representation of the Bethe wave functions via the Schur functions allows to apply the well-developed theory of the symmetric functions to the calculation of the thermal correlation functions. The determinantal expressions of the form-factors and of the thermal correlation functions are obtained. The q-binomial determinants enable the connection of the form-factors with the generating functions both of boxed plane partitions and of self-avoiding lattice paths. The asymptotical behavior of the thermal correlation functions is studied in the limit of low temperature provided that the characteristic parameters of the system are large enough.
Correlation Functions of XX0 Heisenberg Chain, q-Binomial Determinants, and Random Walks
Bogoliubov, N M
2014-01-01
The XX0 Heisenberg model on a cyclic chain is considered. The representation of the Bethe wave functions via the Schur functions allows to apply the well-developed theory of the symmetric functions to the calculation of the thermal correlation functions. The determinantal expressions of the form-factors and of the thermal correlation functions are obtained. The q-binomial determinants enable the connection of the form-factors with the generating functions both of boxed plane partitions and of self-avoiding lattice paths. The asymptotical behavior of the thermal correlation functions is studied in the limit of low temperature provided that the characteristic parameters of the system are large enough.
Correlation functions of XX0 Heisenberg chain, q-binomial determinants, and random walks
Bogoliubov, N. M.; Malyshev, C.
2014-02-01
The XX0 Heisenberg model on a cyclic chain is considered. The representation of the Bethe wave functions via the Schur functions allows to apply the well-developed theory of the symmetric functions to the calculation of the thermal correlation functions. The determinantal expressions of the form-factors and of the thermal correlation functions are obtained. The q-binomial determinants enable the connection of the form-factors with the generating functions both of boxed plane partitions and of self-avoiding lattice paths. The asymptotical behavior of the thermal correlation functions is studied in the limit of low temperature provided that the characteristic parameters of the system are large enough.
Global bipartite entanglement in the three-qubit heisenberg XXX spin chain with impurity
We study the global bipartite entanglement of the three-qubit Heisenberg XXX spin chain with impurity. Through calculating the negativities N1-23 and N12-3, we show that the critical temperature Tc above which the entanglement vanishes increases with the increase of the impurity parameter J1. For a given T, the corresponding critical impurity parameter J1c below which the entanglement vanishes increases with the increase of the magnetic field B, and by adjusting J1 and B one can control the values of N1-23 and N12-3. The maximum value of N12-3 decreases from 0.5 to 0.3727 as the temperature rises, but the one of N1-23 keeps the constant value of about 0.4714. (authors)
Local Magnetization in the Impure Spin 1/2 Anisotropic Ising-Heisenberg Chains
Gildenblat, Gennady
A theory of the Friedel-type oscillations of the local magnetization in the impure antiferromagnetic spin 1/2 chains is developed using the Green function equations of motion in the pseudo-fermion representation. For the isotropic XY (XX) chain, the problem is solved exactly, while the Ising-Heisenberg model is investigated numerically within a temperature-dependent Hartree-Fock approximation. It is shown that the Hartree-Fock self consistency equations for the uniformly magnetized XXZ chain can be recovered as a particular case of the formalism developed in the present work. Comparison with the earlier perturbation theory treatment in a free-fermion approximation reveals that the magnetic field dependence of the perturbation of the local magnetization is sensitive to the formation of the localized states and the exact form of the energy dispersion law of the quasi-particles. In particular it is shown that the perturbations of the local magnetization in the impure spin 1/2 chains disappear in the absence of the external magnetic field. Using the exact solution for the XY chain it is shown that unless the localized energy levels are formed outside the pseudo-fermion energy band the singularity of the local magnetization existing in the pure chain disappears at an arbitrary distance from the single impurity spin. For the ferromagnetic chain with the ferromagnetically coupled impurity the solution of the Hartree-Fock equations at low temperatures agrees reasonably with the results of the linear spin-wave theory. If the impurity is antiferromagnetically coupled, then, in contrast with the results of the spin -wave theory, the Hartree-Fock approximation agrees with the exact result for the zero-field ground state spin defect at the impurity site. Unlike the previous methods, the technique developed in this work permits investigation of the whole temperature range and predicts the correct Curie-Weiss behavior at sufficiently large temperatures.
Zhang, J; Zhang, W; Deng, Z; Liu, W; Lü, Z; Zhang, Jingfu; Long, Gui Lu; Zhang, Wei; Deng, Zhiwei; Liu, Wenzhang; Lu, Zhiheng
2005-01-01
The three- spin chain with Heisenberg XY- interaction is simulated in a three- qubit nuclear magnetic resonance (NMR) quantum computer. The evolution caused by the XY- interaction is decomposed into a series of single- spin rotations and the $J$- coupling evolutions between the neighboring spins. The perfect state transfer (PST) algorithm proposed by M. Christandl et al [Phys. Rev. Lett, 92, 187902(2004)] is realized in the XY- chain.
Rao, K. Rama Koteswara; Kumar, Anil
2011-01-01
The evolution of entanglement in a 3-spin chain with nearest-neighbor Heisenberg-XY interactions for different initial states is investigated here. In an NMR experimental implementation, we generate multipartite entangled states starting from initial separable pseudo-pure states by simulating nearest-neighbor XY interactions in a 3-spin linear chain of nuclear spin qubits. For simulating XY interactions, we follow algebraic method of Zhang et al. [Phys. Rev. A 72, 012331 (2005)]. Bell state b...
Exactly solved mixed spin-(1,1/2) Ising–Heisenberg diamond chain with a single-ion anisotropy
The mixed spin-(1,1/2) Ising–Heisenberg diamond chain with a single-ion anisotropy is exactly solved through the generalized decoration–iteration transformation and the transfer-matrix method. The decoration–iteration transformation is first used for establishing a rigorous mapping equivalence with the corresponding spin-1 Blume–Emery–Griffiths chain, which is subsequently exactly treated within the transfer-matrix technique. Apart from three classical ground states the model exhibits three striking quantum ground states in which a singlet-dimer state of the interstitial Heisenberg spins is accompanied either with a frustrated state or a polarized state or a non-magnetic state of the nodal Ising spins. It is evidenced that two magnetization plateaus at zero and/or one-half of the saturation magnetization may appear in low-temperature magnetization curves. The specific heat may display remarkable temperature dependences with up to three and four distinct round maxima in a zero and non-zero magnetic field, respectively. - Highlights: • Mixed spin-(1,1/2) Ising–Heisenberg diamond chain is exactly solved. • Quantum ground states with a singlet-dimer state of the Heisenberg spins are found. • Magnetization curve displays intermediate plateaus at zero and half of full magnetization. • Thermal dependences of specific heat may display up to four distinct peaks
Vanishing spin stiffness in the spin-1/2 Heisenberg chain for any nonzero temperature
Carmelo, J. M. P.; Prosen, T.; Campbell, D. K.
2015-10-01
Whether at the zero spin density m =0 and finite temperatures T >0 the spin stiffness of the spin-1 /2 X X X chain is finite or vanishes remains an unsolved and controversial issue, as different approaches yield contradictory results. Here we explicitly compute the stiffness at m =0 and find strong evidence that it vanishes. In particular, we derive an upper bound on the stiffness within a canonical ensemble at any fixed value of spin density m that is proportional to m2L in the thermodynamic limit of chain length L →∞ , for any finite, nonzero temperature, which implies the absence of ballistic transport for T >0 for m =0 . Although our method relies in part on the thermodynamic Bethe ansatz (TBA), it does not evaluate the stiffness through the second derivative of the TBA energy eigenvalues relative to a uniform vector potential. Moreover, we provide strong evidence that in the thermodynamic limit the upper bounds on the spin current and stiffness used in our derivation remain valid under string deviations. Our results also provide strong evidence that in the thermodynamic limit the TBA method used by X. Zotos [Phys. Rev. Lett. 82, 1764 (1999), 10.1103/PhysRevLett.82.1764] leads to the exact stiffness values at finite temperature T >0 for models whose stiffness is finite at T =0 , similar to the spin stiffness of the spin-1 /2 Heisenberg chain but unlike the charge stiffness of the half-filled 1D Hubbard model.
The effect of weak measurement (WM) and quantum measurement reversal (QMR) on the entanglement transfer in two parallel Heisenberg spin chains is investigated. We find that the entanglement transfer can be enhanced by the WM and QMR control for different N (N is the length of each spin chain) and m (m denotes the mth spin pair). More interestingly, we also find that, in the thermodynamic limit where the so-called phase-shift control is invalid, the WM and QMR control is instead very effective. So this investigation indicates that the WM and QMR approach has potential applications in quantum information processing based on the spin chain. (paper)
Quantum teleportation via a two-qubit Heisenberg XXZ chain-effects of anisotropy and magnetic field
ZHOU, YUE; Zhang, Guofeng
2008-01-01
We study quantum teleportation via a two-qubit Heisenberg XXZ chain under an inhomogeneous magnetic field. We first consider entanglement teleportation, and then focus on the teleportation fidelity under different conditions. The effects of anisotropy and the magnetic field, both uniform and inhomogeneous, are discussed. We also find that, though entanglement teleportation does require an entangled quantum channel, a nonzero critical value of minimum entanglement is not always necessary.
This paper investigates the entanglement of a two-qutrit Heisenberg XXX chain with nonlinear couplings under an inhomogeneous magnetic field. By the concept of negativity, we find that the critical temperature increases with the increase of inhomogeneous magnetic field b. Our study indicates that for any |K| > |J|, or |K| < |J| entanglement always exists for certain regions. We also find that at the critical point, the entanglement becomes a nonanalytic function of B and a quantum phase transition occurs. (general)
For the XXX Heisenberg spin-1/2 finite chain with integrable open boundary, the scalar products and the norm of Bethe eigenstates are computed directly in the F-basis. The results are represented as determinants of usual functions of the parameters of the model. The Gaudin formula for the square of the norm of the Bethe wave functions is proved for the case of integrable open boundary condition
Ananikian, N. S.; Hovhannisyan, V. V.
2012-01-01
The exactly solvable spin-1/2 Ising-Heisenberg model on diamond chain has been considered. We have found the exact results for the magnetization by using recursion relation method. The existence of the magnetization plateau has been observed at one third of the saturation magnetization in the antiferromagnetic case. Some ground-state properties of the model are examined. At low temperatures, the system has two ferrimagnetic (FRI1 and FRI2) phases and one paramagnetic (PRM) phase. Lyapunov exp...
Thermodynamic limit of particle-hole form factors in the massless XXZ Heisenberg chain
We study the thermodynamic limit of the particle-hole form factors of the XXZ Heisenberg chain in the massless regime. We show that, in this limit, such form factors decrease as an explicitly computed power-law in the system size. Moreover, the corresponding amplitudes can be obtained as a product of a ''smooth'' and a ''discrete'' part: the former depends continuously on the rapidities of the particles and holes, whereas the latter has an additional explicit dependence on the set of integer numbers that label each excited state in the associated logarithmic Bethe equations. We also show that special form factors corresponding to zero-energy excitations lying on the Fermi surface decrease as a power-law in the system size with the same critical exponents as in the longdistance asymptotic behavior of the related two-point correlation functions. The methods we develop in this article are rather general and can be applied to other massless integrable models associated to the six-vertex R-matrix and having determinant representations for their form factors. (orig.)
Thermodynamic limit of particle-hole form factors in the massless XXZ Heisenberg chain
Kitanine, N. [Univ. de Bourgogne (France). IMB, UMR 5584 du CNRS; Kozlowski, K.K. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Maillet, J.M.; Terras, V. [ENS Lyon (France). UMR 5672 du CNRS, Lab. de Physique; Slavnov, N.A. [Steklov Mathematical Inst., Moscow (Russian Federation)
2011-03-15
We study the thermodynamic limit of the particle-hole form factors of the XXZ Heisenberg chain in the massless regime. We show that, in this limit, such form factors decrease as an explicitly computed power-law in the system size. Moreover, the corresponding amplitudes can be obtained as a product of a ''smooth'' and a ''discrete'' part: the former depends continuously on the rapidities of the particles and holes, whereas the latter has an additional explicit dependence on the set of integer numbers that label each excited state in the associated logarithmic Bethe equations. We also show that special form factors corresponding to zero-energy excitations lying on the Fermi surface decrease as a power-law in the system size with the same critical exponents as in the longdistance asymptotic behavior of the related two-point correlation functions. The methods we develop in this article are rather general and can be applied to other massless integrable models associated to the six-vertex R-matrix and having determinant representations for their form factors. (orig.)
Long range anti-ferromagnetic spin model for prebiotic evolution
Nokura, Kazuo [Shonan Institute of Technology, Fujisawa 251-8511 (Japan)
2003-11-28
I propose and discuss a fitness function for one-dimensional binary monomer sequences of macromolecules for prebiotic evolution. The fitness function is defined by the free energy of polymers in the high temperature random coil phase. With repulsive interactions among the same kind of monomers, the free energy in the high temperature limit becomes the energy function of the one-dimensional long range anti-ferromagnetic spin model, which is shown to have a dynamical phase transition and glassy states.
Long range anti-ferromagnetic spin model for prebiotic evolution
I propose and discuss a fitness function for one-dimensional binary monomer sequences of macromolecules for prebiotic evolution. The fitness function is defined by the free energy of polymers in the high temperature random coil phase. With repulsive interactions among the same kind of monomers, the free energy in the high temperature limit becomes the energy function of the one-dimensional long range anti-ferromagnetic spin model, which is shown to have a dynamical phase transition and glassy states
Spontaneous pattern formation in an anti-ferromagnetic quantum gas
Kronjäger, Jochen; Becker, Christoph; Soltan-Panahi, Parvis; Bongs, Kai; Sengstock, Klaus
2009-01-01
Spontaneous pattern formation is a phenomenon ubiquitous in nature, examples ranging from Rayleigh-Benard convection to the emergence of complex organisms from a single cell. In physical systems, pattern formation is generally associated with the spontaneous breaking of translation symmetry and is closely related to other symmetry-breaking phenomena, of which (anti-)ferromagnetism is a prominent example. Indeed, magnetic pattern formation has been studied extensively in both solid-state mater...
The effects of the different Dzyaloshinskii—Moriya (DM) interaction on thermal entanglement of a two-qutrit Heisenberg XX spin chain in a nonuniform magnetic field are investigated. Our results imply that the x-component DM interaction plays a central role in enhancing quantum entanglement and it has a higher critical temperature than the z-component DM interaction. The entanglement can be tunable controlled by changing the multiple of the magnetic fields B1 and B2. Also we found that different DM interaction are competitive to each other in some conditions.
Li, Yan-Chao; Zhu, Yuan-Hui; Yuan, Zi-Gang
2016-03-01
Using the density matrix renormalization group (DMRG) technique, we study the Berezinskii-Kosterlitz-Thouless (BKT) quantum phase transition (QPT) in the J1-J2 Heisenberg chain model from the quantum entanglement point of view. It is found that the gap behavior between two neighboring two-site entanglement entropies as well as the first derivative of both the two-site entropy and the block entropy can be used as indicators for the BKT phase transition in this model. The corresponding size dependent scaling behaviors are analyzed, respectively. Our numerical results give direct evidence for the effectiveness of the entanglement in the BKT-type QPT indicating from different aspects.
The integrability of one dimensional classical continuum inhomogeneous biquadratic Heisenberg spin chain and the effect of nonlinear inhomogeneity on the soliton of an underlying completely integrable spin model are studied. The dynamics of the spin system is expressed in terms of a higher order generalized nonlinear Schroedinger equation through a differential geometric approach which becomes integrable for a particular choice of the biquadratic exchange interaction and for linear inhomogeneity. The effect of nonlinear inhomogeneity on the spin soliton is studied by carrying out a multiple scale perturbation analysis. (author)
Dhar, Abhishek; Sriram Shastry, B.
2000-09-01
We present a calculation of the lowest excited states of the Heisenberg ferromagnet in 1D for any wave vector. These turn out to be string solutions of Bethe's equations with a macroscopic number of particles in them. They are identified as generalized quantum Bloch wall states, and a simple physical picture is provided for the same.
Dhar, Abhishek; Shastry, B. Sriram
2000-01-01
We present a calculation of the lowest excited states of the Heisenberg ferromagnet in 1-d for any wave vector. These turn out to be string solutions of Bethe's equations with a macroscopic number of particles in them. These are identified as generalized quantum Bloch wall states, and a simple physical picture provided for the same.
For one-dimensional quantum spin chain systems recent experimental and theoretical studies indicate unexpectedly large, in some cases diverging spin and heat transport coefficients. Local probes, like e.g. muon spin relaxation (μSR) can indirectly characterize the spin transport properties of low dimensional systems via the magnetic field dependence of the spin lattice relaxation rate λ(B). For diffusive spin transport λ∝B-0.5 is expected. For the ground state of the isotropic spin-1/2 antiferromagnetic Heisenberg chain the eigenstates of the Heisenberg Hamiltonian dominate the spin transport, which is then ballistic. Using the Mueller ansatz λ∝B-1 is expected in this case. For SrCuO2 we find λ∝B-0.9(3). This result is temperature independent for 5 K≤T ≤300 K. Within conformal field theory and using the Mueller ansatz we conclude ballistic spin transport in SrCuO2.
Ground-State and Thermal Entanglement in Three-Spin Heisenberg-XXZ Chain with Three-Spin Interaction
无
2007-01-01
The entanglement properties of a three-spin X X Z Heisenberg chain with three-spin interaction are studied by means of concurrence of pairwise entanglement. We show that ground-state pairwise entanglement, pairwise thermal entanglement, or quantum phase transition is not present in antiferromagnetic spin chain. For the ferromagnetic case, quantum phase transition takes place at △ = 1 for anisotropic interaction and at some values of three-spin coupling strength, and pairwise thermal entanglement increases when the value of J/T increases and with anisotropic interaction and three-spin interaction decrease. In addition, we find that increasing the anisotropic interaction and the three-spin interaction will decrease critical temperature.
Berruto, F; Semenoff, Gordon W; Sodano, P
1999-01-01
We study the strong coupling limit of the 2-flavor massless Schwinger model on a lattice using staggered fermions and the Hamiltonian approach to lattice gauge theories. Using the correspondence between the low-lying states of the 2-flavor strongly coupled lattice Schwinger model and the antiferromagnetic Heisenberg chain established in a previous paper, we explicitly compute the mass gaps of the other excitations in terms of vacuum expectation values (v.e.v.'s) of powers of the Heisenberg Hamiltonian and spin-spin correlation functions. We find a satisfactory agreement with the results of the continuum theory already at the second order in the strong coupling expansion. We show that the pattern of symmetry breaking of the continuum theory is well reproduced by the lattice theory; we see indeed that in the lattice theory the isoscalar and isovector chiral condensates are zero to every order in the strong coupling expansion. In addition, we find that the chiral condensate $$ is non zero also on the lattice; th...
Entanglement dynamics of a Heisenberg chain with Dzyaloshinski-Moriya interaction
Zheng qiang; Zhang Xiao-Ping; Zhi Qi-Jun; Ren Zhong-Zhou
2009-01-01
This paper investigates the entanglement dynamics of the system,composed of two qubits A and B with Heisenberg XX spin interactation.There is a third controller qubit C,which only has Dzyaloshiuskii-Moriya (DM) spin-orbit interaction with the qubit B.It is found that depending on the initial state of the controller qubit C and DM interaction,the entanglement of the system displays amplification and sudden birth effects.These effects indicate that one can control the entanglement of the system,which may be helpful for quantum information processing.
Motion of a magnetic soliton about a lattice soliton in a Heisenberg chain
As an example of interaction between two solitons belonging to different species, a semiclassical study of the nonlinear dynamics of a coupled magnon-phonon system in a one-dimensional Heisenberg ferromagnet is made, where both the lattice and the spin systems are taken with their respective nonlinear interactions. The lattice soliton is shown to introduce spatial inhomogeneities into the propagation of the magnetic soliton resulting in (a) the trapping of the magnetic soliton in the harmonic field of the lattice soliton and (b) the amplitude and the width of the magnetic soliton becoming time-dependent. (author)
Slow quenches in XXZ spin-chains -- the role of Galilean invariance breaking
Chudzinski, P.
2016-01-01
We study a XXZ spin-chain in a gapless Tomonaga-Luttinger liquid (TLL) phase with time dependent anisotropy of spin exchange interactions. To begin we focus on a linear ramp of $J_z$, starting at XX point and slowly increasing towards the anti-ferromagnetic Heisenberg point. Although the problem of a linear ramp in the TLL has been recently under intense scrutiny in a perturbative \\emph{g-ology} framework, an aspect that has been overlooked so far is the role of the Galilean invariance breaki...
The finite-size spectra of the spin-1/2 XXZ Heisenberg chain with toroidal boundary conditions and an even number of sites provide a projection mechanism yielding the spectra of models with central charge cq[sl(2)] quantum algebra transformations. (author)
Impurity effects in a S=1/2 Heisenberg spin chain probed by {sup 63}Cu NMR
Utz, Yannic; Bruening, Eva Maria; Hammerath, Franziska; Rudisch, Christian; Grafe, Hans-Joachim; Mohan, Ashwin; Hess, Christian; Nishimoto, Satoshi; Drechsler, Stefan-Ludwig; Buechner, Bernd [IFW Dresden (Germany); Saint-Martin, Romuald; Revcolevschi, Alexandre [LPCES, Orsay (France)
2013-07-01
We present {sup 63}Cu NMR measurements on undoped, Ni doped and Mg doped SrCuO{sub 2} single crystals. SrCuO{sub 2} is a good realization of a one-dimensional S=1/2 Heisenberg spin chain. This is confirmed by the theoretically-expected temperature independent NMR spin-lattice relaxation rate T{sup -1}{sub 1}. Doping with Ni, which can be regarded as a S=1 impurity, has a major impact on the magnetic properties of the spin chains. On the one hand, this is manifested by unusual features in the NMR spectra below 100 K, revealing the existence of an impurity-induced local alternating magnetisation. On the other hand, exponentially decaying spin lattice relaxation rates towards low temperatures indicate the opening of a spin gap similar to Ca doped SrCuO{sub 2}. Mg doping (S=0) has, however, no influence on the magnetic properties of the spin chains. Neither the NMR spectra nor the spin lattice relaxation rates differ from those measured on pure SrCuO{sub 2}. While the different impact of Ni and Mg doping on the spin chains could be explained by their different impurity spins, the opening of a spin gap in case of Ni doping is totally unexpected and not yet understood.
Huang Li-Yuan; Fang Mao-Fa
2008-01-01
The thermal entanglement and teleportation of a thermally mixed entangled state of a two-qubit Heisenberg XXX chain under the Dzyaloshinski-Moriya (DM) anisotropic antisymmetric interaction through a noisy quantum channel given by a Werner state is investigated. The dependences of the thermal entanglement of the teleported state on the DM coupling constant, the temperature and the entanglement of the noisy quantum channel are studied in detail for both the ferromagnetic and the antiferromagnetic cases. The result shows that a minimum entanglement of the noisy quantum channel must be provided in order to realize the entanglement teleportation. The values of fidelity of the teleported state are also studied for these two cases. It is found that under certain conditions, we can transfer an initial state with a better fidelity than that for any classical communication protocol.
Natural thermal entanglement between two qubits with XXX Heisenberg interaction is studied. For the antiferromagnet, increasing coupling strength or decreasing temperature under critical point increases the entanglement. Based on the thermal entanglement as quantum channel, entanglement and information of an input entangled state are transferred via partial teleportation. We find that the entanglement transferred will be lost during the process, and for the entanglement fidelity the partial teleportation is superior to classical communication as concurrence of entangled channel beyond 1/4. We show that both correlation information in input entangled state and individual information of the teleported particle are linearly dissipated. With more entanglement in quantum channel, more entanglement and correlation information can be transferred.
Ba2Cu2Te2P2O13: A new telluro-phosphate with S=1/2 Heisenberg chain
A new telluro-phosphate compound Ba2Cu2Te2P2O13 with S=1/2 Heisenberg chain has been successfully synthesized by solid state reaction and grown by flux method. Single crystal X-ray diffraction reveals that Ba2Cu2Te2P2O13 crystallizes into a monoclinic space group C2/c and cell parameters of a=17.647(3) Å, b=7.255(2) Å, c=9.191(2) Å and β=100.16 (3)°. In the structure of Ba2Cu2Te2P2O13, one dimensional [CuTePO7]3− chains are formed by tetrahedral PO4 and trigonal bi-pyramidal TeO4 joining square planar CuO4 groups. Those [CuTePO7]3− chains are inter-connected by sharing one oxygen atom from the TeO4 group to form two dimensional layers. Magnetic susceptibility and specific heat measurements confirm that the title compound is a model one dimensional Heisenberg antiferromagnetic chain system. - Graphical abstract: Ba2Cu2Te2P2O13, containing (CuTePO7)3− chains formed by PO4 and TeO4 joining CuO4 groups, shows typical 1D Heisenberg antiferromagnetic chain model behavior as confirmed by magnetic measurements. - Highlights: • New telluro-phosphate Ba2Cu2Te2P2O13 has been grown. • It features layered structure composed of [CuTePO7]3− chains and TeO4 groups. • It shows the Heisenberg antiferromagnetic chain behavior. • It is transparent in the range of 1000–2500 nm with a UV absorption edge of 393 nm
Gu, Bo; Su, Gang; Gao, Song
2006-04-01
The magnetization process, the susceptibility, and the specific heat of the spin- 1/2 antiferromagnet (AF)-AF-ferromagnet (F) and F-F-AF trimerized quantum Heisenberg chains have been investigated by means of the transfer matrix renormalization group (TMRG) technique as well as the modified spin-wave (MSW) theory. A magnetization plateau at m=1/6 for both trimerized chains is observed at low temperature. The susceptibility and the specific heat show various behaviors for different ferromagnetic and antiferromagnetic interactions and in different magnetic fields. The TMRG results of susceptibility and the specific heat can be nicely fitted by a linear superposition of double two-level systems, where two fitting equations are proposed. Three branch excitations, one gapless excitation and two gapful excitations, for both systems are found within the MSW theory. It is observed that the MSW theory captures the main characteristics of the thermodynamic behaviors at low temperatures. The TMRG results are also compared with the possible experimental data.
Singular eigenstates in the even(odd) length Heisenberg spin chain
Giri, Pulak Ranjan
2014-01-01
Introducing a regularization scheme, we derive a set of equations for the rapidities of the singular solutions, whose distinct and self-conjugate solutions produce Bethe eigenstates. We obtain singular eigenstates and their corresponding eigenvalues of the transfer matrix of the spin-1/2 XXX chain. For an even length spin-1/2 XXX chain, we show that the singular solutions \\{\\lambda_\\alpha\\} are invariant under the sign changes of their rapidities, \\{\\lambda_\\alpha\\}=\\{-\\lambda_\\alpha\\}. For odd N length spin-1/2 chain in the three down-spin sector, it has been analytically shown that there exist singular solutions in any finite length of the spin chain of the form N= 3\\left(2k+1\\right) with k=1, 2, 3, \\cdots. It is also shown that there exist no singular solutions in the four down-spin sector for some odd length spin-1/2 XXX chains.
Liu, Guang-Hua; Dou, Jun-Ya; Lu, Peng
2016-03-01
The effect of the Dzyaloshinskii-Moriya interaction (DMI) on ground-state phase diagrams of spin-1 Heisenberg-Ising alternating chains is investigated by the infinite time-evolving block decimation method. Three rich phase diagrams for three cases with different DMIs are obtained and discussed systematically. The DMI on even bonds plays a key role in the ground-state phase diagram, especially the appearance of the Haldane phase. However, the DMI on odd bonds seems to have very weak effect on the phase diagram. Both the odd- and even-string orders become nonzero in the Haldane phase, and have their maximum values at θ = π. For the odd-dimer phase, the even-string correlator vanishes absolutely despite varying θ, but a double-peak structure of the odd-string correlator is observed. Odd-string correlator becomes maximum at θ = π / 2 and 3 π / 2, but vanishes at θ = π. It indicates that the generalized string correlator can be used to distinguish the odd-dimer from the Haldane phase. Doubly degenerate entanglement spectrum is observed in the Haldane phase, which can be regarded as a clear signature of the existence of topological orders. Strong enough transverse nearest-neighbor correlations are found to be very important for the appearance of the Haldane and the odd-dimer phases.
Quantum discord and entanglement in Heisenberg XXZ spin chain after quenches
Ren, Jie; Wu, Yin-Zhong; Zhu, Shi-Qun
2012-01-01
Using the adaptive time-dependent density-matrix renormalization group method, the dynamics of entanglement and quantum discord of a one-dimensional spin-1/2 XXZ chain is studied when anisotropic interaction quenches are applied at different temperatures. The dynamics of the quantum discord and pairwise entanglement between the nearest qubits shows that the entanglement and quantum discord will first oscillate and then approach to a constant value. The quantum discord can be used to predict t...
Bethe-ansatz equations for quantum Heisenberg chains with elliptic exchange
Inozemtsev, V. I.
1999-01-01
The eigenvectors of the Hamiltonian ${\\cal H}_{N}$ of $N$-sites quantum spin chains with elliptic exchange are connected with the double Bloch meromorphic solutions of the quantum continuous elliptic Calogero-Moser problem. This fact allows one to find the eigenvectors via the solutions to the system of highly transcendental equations of Bethe-ansatz type which is presented in explicit form.
Liu, Guang-Hua; You, Wen-Long; Li, Wei; Su, Gang
2015-01-01
Quantum phase transitions (QPTs) and the ground-state phase diagram of the spin-1/2 Heisenberg-Ising alternating chain (HIAC) with uniform Dzyaloshinskii-Moriya (DM) interaction are investigated by a matrix-product-state (MPS) method. By calculating the odd- and even-string order parameters, we recognize two kinds of Haldane phases, i.e., the odd- and even-Haldane phases. Furthermore, doubly degenerate entanglement spectra on odd and even bonds are observed in odd- and even-Haldane phases, re...
Excitations and phase transitions in random anti-ferromagnets
Cowley, R.A.; Birgeneau, R.J.; Shirane, G.
1979-01-01
Neutron scattering techniques can be used to study the magnetic excitations and phase transitions in the randomly mixed transition metal fluorides. The results for the excitations of samples with two different types of magnetic ions show two bands of excitations; each associated with excitations propagating largely on one type of ion. In the diluted salts the spectra show a complex line shape and greater widths. These results are in good accord with computer simulations showing that linear spin wave theory can be used, but have not been described satisfactorily using the coherent potential approximation. The phase transitions in these materials are always smeared, but it is difficult to ascertain if this smearing is due to macroscopic fluctuations in the concentration or of an intrinsic origin. Studies of these systems close to the percolation point have shown that the thermal disorder is associated with the one-dimensional weak links of the large clusters. Currently theory and experiment are in accord for the two-dimensional Ising system but features are still not understood in Heisenberg systems in both two and three dimensions.
Excitations and phase transitions in random anti-ferromagnets
Neutron scattering techniques can be used to study the magnetic excitations and phase transitions in the randomly mixed transition metal fluorides. The results for the excitations of samples with two different types of magnetic ions show two bands of excitations; each associated with excitations propagating largely on one type of ion. In the diluted salts the spectra show a complex line shape and greater widths. These results are in good accord with computer simulations showing that linear spin wave theory can be used, but have not been described satisfactorily using the coherent potential approximation. The phase transitions in these materials are always smeared, but it is difficult to ascertain if this smearing is due to macroscopic fluctuations in the concentration or of an intrinsic origin. Studies of these systems close to the percolation point have shown that the thermal disorder is associated with the one-dimensional weak links of the large clusters. Currently theory and experiment are in accord for the two-dimensional Ising system but features are still not understood in Heisenberg systems in both two and three dimensions
Yannouleas, Constantine; Brandt, Benedikt B.; Landman, Uzi
2016-07-01
Advances with trapped ultracold atoms intensified interest in simulating complex physical phenomena, including quantum magnetism and transitions from itinerant to non-itinerant behavior. Here we show formation of antiferromagnetic ground states of few ultracold fermionic atoms in single and double well (DW) traps, through microscopic Hamiltonian exact diagonalization for two DW arrangements: (i) two linearly oriented one-dimensional, 1D, wells, and (ii) two coupled parallel wells, forming a trap of two-dimensional, 2D, nature. The spectra and spin-resolved conditional probabilities reveal for both cases, under strong repulsion, atomic spatial localization at extemporaneously created sites, forming quantum molecular magnetic structures with non-itinerant character. These findings usher future theoretical and experimental explorations into the highly correlated behavior of ultracold strongly repelling fermionic atoms in higher dimensions, beyond the fermionization physics that is strictly applicable only in the 1D case. The results for four atoms are well described with finite Heisenberg spin-chain and cluster models. The numerical simulations of three fermionic atoms in symmetric DWs reveal the emergent appearance of coupled resonating 2D Heisenberg clusters, whose emulation requires the use of a t–J-like model, akin to that used in investigations of high T c superconductivity. The highly entangled states discovered in the microscopic and model calculations of controllably detuned, asymmetric, DWs suggest three-cold-atom DW quantum computing qubits.
Grimm, U; Grimm, Uwe; Schuetz, Gunter M.
1993-01-01
The finite-size scaling spectra of the spin-1/2 XXZ Heisenberg chain with toroidal boundary conditions and an even number of sites provide a projection mechanism yielding the spectra of models with a central charge c<1 including the unitary and non-unitary minimal series. Taking into account the half-integer angular momentum sectors - which correspond to chains with an odd number of sites - in many cases leads to new spinor operators appearing in the projected systems. These new sectors in the XXZ chain correspond to a new type of frustration lines in the projected minimal models. The corresponding new boundary conditions in the Hamiltonian limit are investigated for the Ising model and the 3-state Potts model and are shown to be related to duality transformations which are an additional symmetry at their self-dual critical point. By different ways of projecting systems we find models with the same central charge sharing the same operator content and modular invariant partition function which however diffe...
Ultra-cold Neutron Production in Anti-ferromagnetic Oxygen Solid
Liu, C Y
2004-01-01
Spin waves, or magnons, in the anti-ferromagnetic $\\alpha$ phase of solid oxygen provide a novel mechanism for ultra-cold neutron (UCN) production. Magnons dominate the energy exchange mechanisms for cold neutrons and UCN in solid $\\alpha$-oxygen, much in the same way as do phonons in solid deuterium superthermal UCN sources. We present calculations of UCN production and upscattering rates in S-O$_2$. The results indicate that S-O$_2$ is potentially a much more efficient UCN source material than solid deuterium.
Pearce, D J G; Turner, M S
2015-10-01
Self-propelled particle (SPP) models are often compared with animal swarms. However, the collective animal behaviour observed in experiments often leaves considerable unconstrained freedom in the structure of a proposed model. Essentially, multiple models can describe the observed behaviour of animal swarms in simple environments. To tackle this degeneracy, we study swarms of SPPs in non-trivial environments as a new approach to distinguish between candidate models. We restrict swarms of SPPs to circular (periodic) channels where they polarize in one of two directions (like spins) and permit information to pass through windows between neighbouring channels. Co-alignment between particles then couples the channels (anti-ferromagnetically) so that they tend to counter-rotate. We study channels arranged to mimic a geometrically frustrated anti-ferromagnet and show how the effects of this frustration allow us to better distinguish between SPP models. Similar experiments could therefore improve our understanding of collective motion in animals. Finally, we discuss how the spin analogy can be exploited to construct universal logic gates, and therefore swarming systems that can function as Turing machines. PMID:26423438
Liu, Guang-Hua; You, Wen-Long; Li, Wei; Su, Gang
2015-04-01
Quantum phase transitions (QPTs) and the ground-state phase diagram of the spin-1/2 Heisenberg-Ising alternating chain (HIAC) with uniform Dzyaloshinskii-Moriya (DM) interaction are investigated by a matrix-product-state (MPS) method. By calculating the odd- and even-string order parameters, we recognize two kinds of Haldane phases, i.e. the odd- and even-Haldane phases. Furthermore, doubly degenerate entanglement spectra on odd and even bonds are observed in odd- and even-Haldane phases, respectively. A rich phase diagram including four different phases, i.e. an antiferromagnetic (AF), AF stripe, odd- and even-Haldane phases, is obtained. These phases are found to be separated by continuous QPTs: the topological QPT between the odd- and even-Haldane phases is verified to be continuous and corresponds to conformal field theory with central charge c = 1 while the rest of the phase transitions in the phase diagram are found to be c = 1/2. We also revisit, with our MPS method, the exactly solvable case of HIAC model with DM interactions only on odd bonds and find that the even-Haldane phase disappears, but the other three phases, i.e. the AF, AF stripe and odd-Haldane phases, still remain in the phase diagram. We exhibit the evolution of the even-Haldane phase by tuning the DM interactions on the even bonds gradually.
Numerical investigation of correlation functions for the UqSU(2) invariant spin-1/2 Heisenberg chain
We consider the UqSU(2) invariant spin-1/2 XXZ quantum spin chain at the roots of unity q=exp(i π/(m+1)), corresponding to different minimal models of conformal field theory. We conduct a numerical investigation of the correlation functions of UqSU(2) scalar two-point operators in order to find which operators in the minimal models they correspond to. Using graphical representations of the Temperley-Lieb algebra we are able to deal with chains of up to 28 sites. Depending on q, the correlation functions show different characteristics and finite-size behaviour. For m=2/3, which corresponds to the Lee-Yang edge singularity, we find the surface and bulk critical exponent -1/5. Together with the known result in the case m=3 (Ising model) this indicates that in the continuum limit the two-point operators involve conformal fields of spin-m-1/m+1. For other roots of unity q the chains are too short to determine the surface and bulk critical exponents. (author)
Ba{sub 2}Cu{sub 2}Te{sub 2}P{sub 2}O{sub 13}: A new telluro-phosphate with S=1/2 Heisenberg chain
Xia, Mingjun [Beijing Center for Crystal Research and Development, Key Laboratory of Functional Crystals and Laser Technology, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100190 (China); Shen, Shipeng; Lu, Jun; Sun, Young [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Li, R.K., E-mail: rkli@mail.ipc.ac.cn [Beijing Center for Crystal Research and Development, Key Laboratory of Functional Crystals and Laser Technology, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100190 (China)
2015-10-15
A new telluro-phosphate compound Ba{sub 2}Cu{sub 2}Te{sub 2}P{sub 2}O{sub 13} with S=1/2 Heisenberg chain has been successfully synthesized by solid state reaction and grown by flux method. Single crystal X-ray diffraction reveals that Ba{sub 2}Cu{sub 2}Te{sub 2}P{sub 2}O{sub 13} crystallizes into a monoclinic space group C2/c and cell parameters of a=17.647(3) Å, b=7.255(2) Å, c=9.191(2) Å and β=100.16 (3)°. In the structure of Ba{sub 2}Cu{sub 2}Te{sub 2}P{sub 2}O{sub 13}, one dimensional [CuTePO{sub 7}]{sup 3−} chains are formed by tetrahedral PO{sub 4} and trigonal bi-pyramidal TeO{sub 4} joining square planar CuO{sub 4} groups. Those [CuTePO{sub 7}]{sup 3−} chains are inter-connected by sharing one oxygen atom from the TeO{sub 4} group to form two dimensional layers. Magnetic susceptibility and specific heat measurements confirm that the title compound is a model one dimensional Heisenberg antiferromagnetic chain system. - Graphical abstract: Ba{sub 2}Cu{sub 2}Te{sub 2}P{sub 2}O{sub 13}, containing (CuTePO{sub 7}){sup 3−} chains formed by PO{sub 4} and TeO{sub 4} joining CuO{sub 4} groups, shows typical 1D Heisenberg antiferromagnetic chain model behavior as confirmed by magnetic measurements. - Highlights: • New telluro-phosphate Ba{sub 2}Cu{sub 2}Te{sub 2}P{sub 2}O{sub 13} has been grown. • It features layered structure composed of [CuTePO{sub 7}]{sup 3−} chains and TeO{sub 4} groups. • It shows the Heisenberg antiferromagnetic chain behavior. • It is transparent in the range of 1000–2500 nm with a UV absorption edge of 393 nm.
Ni, Hui-Ying; Fang, Jian-Xing; Zhu, Shi-Qun; Sha, Jin-Qiao; Jiang, Wei-Xing
2008-02-01
In this paper we study the entanglement in a two-qubit spin in the XYZ model, and teleport a two-qubit entangled state using this spin chain in the condition of the thermal equilibrium as a quantum channel. We investigate the effects of the interaction of z-component JZ, the inhomogeneous magnetic field b, the anisotropy γ, and the temperature T on the entanglement and fidelity. In order to characterize the quality of the teleported state, we research the average fidelity Fa. High average fidelity of the teleportation is obtained when the temperat ure is very low. Under some condition, we also find that when inhomogeneity increases to a certain value, the average fidelity can exhibit a larger revival than that for less values of b.
Thermal entanglement in a four-qubit Heisenberg spin model with external magnetic fields
The entanglement properties both in the four-qubit anisotropic Heisenberg XY chain with uniform external magnetic fields and in the Heisenberg XX model with two external fields are investigated. The analytical expressions for the measures of entanglement are obtained. In Heisenberg XY chain, the effects of the anisotropy on the thermal entanglement are studied. In the Heisenberg XX ring with two external fields, it is found that a high pair entanglement can be obtained
Thermal entanglement in a four-qubit Heisenberg spin model with external magnetic fields
Wu, Ke-Dong; Zhou, Bin; Cao, Wan-Qiang
2007-03-01
The entanglement properties both in the four-qubit anisotropic Heisenberg XY chain with uniform external magnetic fields and in the Heisenberg XX model with two external fields are investigated. The analytical expressions for the measures of entanglement are obtained. In Heisenberg XY chain, the effects of the anisotropy on the thermal entanglement are studied. In the Heisenberg XX ring with two external fields, it is found that a high pair entanglement can be obtained.
Pb2MnTeO6 Double Perovskite: An Antipolar Anti-ferromagnet.
Retuerto, Maria; Skiadopoulou, Stella; Li, Man-Rong; Abakumov, Artem M; Croft, Mark; Ignatov, Alexander; Sarkar, Tapati; Abbett, Brian M; Pokorný, Jan; Savinov, Maxim; Nuzhnyy, Dmitry; Prokleška, Jan; Abeykoon, Milinda; Stephens, Peter W; Hodges, Jason P; Vaněk, Přemysl; Fennie, Craig J; Rabe, Karin M; Kamba, Stanislav; Greenblatt, Martha
2016-05-01
Pb2MnTeO6, a new double perovskite, was synthesized. Its crystal structure was determined by synchrotron X-ray and powder neutron diffraction. Pb2MnTeO6 is monoclinic (I2/m) at room temperature with a regular arrangement of all the cations in their polyhedra. However, when the temperature is lowered to ∼120 K it undergoes a phase transition from I2/m to C2/c structure. This transition is accompanied by a displacement of the Pb atoms from the center of their polyhedra due to the 6s(2) lone-pair electrons, together with a surprising off-centering of Mn(2+) (d(5)) magnetic cations. This strong first-order phase transition is also evidenced by specific heat, dielectric, Raman, and infrared spectroscopy measurements. The magnetic characterizations indicate an anti-ferromagnetic (AFM) order below TN ≈ 20 K; analysis of powder neutron diffraction data confirms the magnetic structure with propagation vector k = (0 1 0) and collinear AFM spins. The observed jump in dielectric permittivity near ∼150 K implies possible anti-ferroelectric behavior; however, the absence of switching suggests that Pb2MnTeO6 can only be antipolar. First-principle calculations confirmed that the crystal and magnetic structures determined are locally stable and that anti-ferroelectric switching is unlikely to be observed in Pb2MnTeO6. PMID:27058393
Remark on Heisenberg's principle
Application of Heisenberg's principle to inertial frame transformations allows a distinction between three commutative groups of reciprocal transformations along one direction: Galilean transformations, dual transformations, and Lorentz transformations. These are three conjugate groups and for a given direction, the related commutators are all proportional to one single conjugation transformation which compensates for uniform and rectilinear motions. The three transformation groups correspond to three complementary ways of measuring space-time as a whole. Heisenberg's Principle then gets another explanation
Heisenberg's observability principle
Wolff, JE
2014-01-01
Werner Heisenberg's 1925 paper ‘Quantum-theoretical re-interpretation of kinematic and mechanical relations’ marks the beginning of quantum mechanics. Heisenberg famously claims that the paper is based on the idea that the new quantum mechanics should be ‘founded exclusively upon relationships between quantities which in principle are observable’. My paper is an attempt to understand this observability principle, and to see whether its employment is philosophically defensible. Against interpr...
HEISENBERG'S INEQUALITY AND LOGARITHMIC HEISENBERG'S INEQUALITY FOR AMBIGUITY FUNCTION
Tian Guji
2000-01-01
In this article we discuss the relation between Heisenberg's inequality and logarithmic Heisenberg's (entropy) inequality for ambiguity function. After building up a Heisenberg's inequality, we obtain a connection of variance with entropy by variational method. Using classical Taylor's expansion, we prove that the equality in Heisenberg's inequality holds if and only if the entropy of 2k - 1 order is equal to (2k - 1)!.
For describing the dynamics of alpha helical proteins with internal molecular excitations, nonlinear couplings between lattice vibrations and molecular excitations, and spin excitations in one-dimensional isotropic biquadratic Heisenberg ferromagnetic spin with the octupole–dipole interactions, we consider an inhomogeneous generalized fourth-order nonlinear Schrödinger equation. Based on the Ablowitz–Kaup–Newell–Segur system, infinitely many conservation laws for the equation are derived. Through the auxiliary function, bilinear forms and N-soliton solutions for the equation are obtained. Interactions of solitons are discussed by means of the asymptotic analysis. Effects of linear inhomogeneity on the interactions of solitons are also investigated graphically and analytically. Since the inhomogeneous coefficient of the equation h=α x+β, the soliton takes on the parabolic profile during the evolution. Soliton velocity is related to the parameter α, distance scale coefficient and biquadratic exchange coefficient, but has no relation with the parameter β. Soliton amplitude and width are only related to α. Soliton position is related to β
The chirality operators for Heisenberg spin systems
The ground state of closed Heisenberg spin chains with an odd number of sites has a chiral degeneracy, in addition to a two-fold Kramers degeneracy. A non-zero chirality implies that the spins are not coplanar, and is a measure of handedness. The chirality operator, which can be treated as a spin-1/2 operator, is explicitly constructed in terms of the spin operators, and is given as commutator of permutation operators. (author). 3 refs
Yang, Jin-Wei; Gao, Yi-Tian; Wang, Qi-Min; Su, Chuan-Qi; Feng, Yu-Jie; Yu, Xin
2016-01-01
In this paper, a fourth-order variable-coefficient nonlinear Schrödinger equation is studied, which might describe a one-dimensional continuum anisotropic Heisenberg ferromagnetic spin chain with the octuple-dipole interaction or an alpha helical protein with higher-order excitations and interactions under continuum approximation. With the aid of auxiliary function, we derive the bilinear forms and corresponding constraints on the variable coefficients. Via the symbolic computation, we obtain the Lax pair, infinitely many conservation laws, one-, two- and three-soliton solutions. We discuss the influence of the variable coefficients on the solitons. With different choices of the variable coefficients, we obtain the parabolic, cubic, and periodic solitons, respectively. We analyse the head-on and overtaking interactions between/among the two and three solitons. Interactions between a bound state and a single soliton are displayed with different choices of variable coefficients. We also derive the quasi-periodic formulae for the three cases of the bound states.
Deguchi, Tetsuo; Ranjan Giri, Pulak
2016-04-01
Every solution of the Bethe-ansatz equations (BAEs) is characterized by a set of quantum numbers, by which we can evaluate it numerically. However, no general rule is known how to give quantum numbers for the physical solutions of BAE. For the spin-1/2 XXX chain we rigorously derive all the quantum numbers for the complete set of the Bethe-ansatz eigenvectors in the two down-spin sector with any chain length N. Here we obtain them both for real and complex solutions. We also show that all the solutions associated with them are distinct. Consequently, we prove the completeness of the Bethe ansatz and give an exact expression for the number of real solutions which correspond to collapsed bound-state solutions (i.e., two-string solutions) in the sector: 2[(N-1)/2-(N/π ){{tan}}-1(\\sqrt{N-1})] in terms of Gauss’ symbol. Moreover, we prove in the sector the scheme conjectured by Takahashi for solving BAE systematically. We also suggest that by applying the present method we can derive the quantum numbers for the spin-1/2 XXZ chain.
HEISENBERG'S INEQUALITY IN SOBOLEV SPACES
无
2000-01-01
Using the correspondence between psedodifferential operator and its symbol,the authors obtain Heisenberg's inequality in Sobolev spaces and therefore a kind of quantitative representation of uncertainty principle.
Xin Yan
2015-07-01
Full Text Available The Schwinger-boson mean-field theory (SBMFT and the linearized tensor renormalization group (LTRG methods are complementarily applied to explore the thermodynamics of the quantum ferromagnetic mixed spin (S, σ chains. It is found that the system has double excitations, i.e. a gapless and a gapped excitation; the low-lying spectrum can be approximated by ω k ∼ S σ 2 ( S + σ J k 2 with J the ferromagnetic coupling; and the gap between the two branches is estimated to be △ ∼ J. The Bose-Einstein condensation indicates a ferromagnetic ground state with magnetization m tot z = N ( S + σ . At low temperature, the spin correlation length is inversely proportional to temperature (T, the susceptibility behaviors as χ = a 1 ∗ 1 T 2 + a 2 ∗ 1 T , and the specific heat has the form of C = c 1 ∗ T − c 2 ∗ T + c 3 ∗ T 3 2 , with ai (i = 1, 2 and ci (i = 1, 2, 3 the temperature independent constants. The SBMFT results are shown to be in qualitatively agreement with those by the LTRG numerical calculations for S = 1 and σ = 1/2. A comparison of the LTRG results with the experimental data of the model material MnIINiII(NO24(en2(en = ethylenediamine, is made, in which the coupling parameters of the compound are obtained. This study provides useful information for deeply understanding the physical properties of quantum ferromagnetic mixed spin chain materials.
Heisenberg symmetry and hypermultiplet manifolds
Antoniadis, Ignatios; Petropoulos, P Marios; Siampos, Konstantinos
2015-01-01
We study the emergence of Heisenberg (Bianchi II) algebra in hyper-K\\"ahler and quaternionic spaces. This is motivated by the r\\^ole these spaces with this symmetry play in $\\mathcal{N}=2$ hypermultiplet scalar manifolds. We show how to construct related pairs of hyper-K\\"ahler and quaternionic spaces under general symmetry assumptions, the former being a zooming-in limit of the latter at vanishing cosmological constant. We further apply this method for the two hyper-K\\"ahler spaces with Heisenberg algebra, which is reduced to $U(1)\\times U(1)$ at the quaternionic level. We also show that no quaternionic spaces exist with a strict Heisenberg symmetry -- as opposed to $\\text{Heisenberg} \\ltimes U(1)$. We finally discuss the realization of the latter by gauging appropriate $Sp(2,4)$ generators in $\\mathcal{N}=2$ conformal supergravity.
Type-I integrable quantum impurities in the Heisenberg model
Doikou, Anastasia
2013-01-01
Type-I quantum impurities are investigated in the context of the integrable Heisenberg model. This type of defects is associated to the (q)-harmonic oscillator algebra. The transmission matrices associated to this particular type of defects are computed via the Bethe ansatz methodology for the XXX model, as well as for the critical and non-critical XXZ spin chain. In the attractive regime of the critical XXZ spin chain the transmission amplitudes for the breathers are also identified.
Wang, Guangmei [Ruhr-Universitat Bochum; Valldor, Martin [Max Plank Institute for Chemical Physics of Solids, Dresden, Germany; Mallick, Bert [Ruhr Universitat Bochum; Mudring, Anja-Verena [Ames Laboratory
2014-01-01
Four open-framework transition-metal phosphates; (NH4)2Co3(HPO4)2F4 (1), (NH4)Co3(HPO4)2(H2PO4)F2 (2), KCo3(HPO4)2(H2PO4)F2 (3), and KFe3(HPO4)2(H2PO4)F2 (4); are prepared by ionothermal synthesis using pyridinium hexafluorophosphate as the ionic liquid. Single-crystal X-ray diffraction analyses reveal that the four compounds contain cobalt/iron–oxygen/fluoride layers with Kagomé topology composed of interlinked face-sharing MO3F3/MO4F2 octahedra. PO3OH pseudo-tetrahedral groups augment the [M3O6F4] (1)/[M3O8F2] layers on both sides to give M3(HPO4)2F4 (1) and M3(HPO4)2F2 (2–4) layers. These layers are stacked along the a axis in a sequence AA…, resulting in the formation of a layer structure for (NH4)2Co3(HPO4)2F4(1). In NH4Co3(HPO4)2(H2PO4)F2 and KM3(HPO4)2(H2PO4)F2, the M3(HPO4)2F2 layers are stacked along the a axis in a sequence AAi… and are connected by [PO3(OH)] tetrahedra, giving rise to a 3-D open framework structure with 10-ring channels along the [001] direction. The negative charges of the inorganic framework are balanced by K+/NH4+ ions located within the channels. The magnetic transition metal cations themselves form layers with stair-case Kagomé topology. Magnetic susceptibility and magnetization measurements reveal that all four compounds exhibit a canted anti-ferromagnetic ground state (Tc = 10 or 13 K for Co and Tc = 27 K for Fe) with different canting angles. The full orbital moment is observed for both Co2+ and Fe2+.
Cosmological implications of Heisenberg's principle
Gonzalo, Julio A
2015-01-01
The aim of this book is to analyze the all important implications of Heisenberg's Uncertainty Principle for a finite universe with very large mass-energy content such as ours. The earlier and main contributors to the formulation of Quantum Mechanics are briefly reviewed regarding the formulation of Heisenberg's Principle. After discussing “indeterminacy” versus ”uncertainty”, the universal constants of physics are reviewed and Planck's units are given. Next, a novel set of units, Heisenberg–Lemaitre units, are defined in terms of the large finite mass of the universe. With the help of Heisenberg's principle, the time evolution of the finite zero-point energy for the universe is investigated quantitatively. Next, taking advantage of the rigorous solutions of Einstein's cosmological equation for a flat, open and mixed universe of finite mass, the most recent and accurate data on the “age” (to) and the expansion rate (Ho) of the universe and their implications are reconsidered.
Heisenberg, his wife s account
A wife tells about her husband life, Werner Heisenberg, Physics Nobel Price in 1932. After a happy childhood, this brilliant student was Albert Einstein, Niels Bohr, Arnold Sommerfeld s student. But at the nazism time, the great physician refused to leave his country, guaranteeing the Hitler regime and taking part in effort of war, that is to say the run to the bomb. The account of Elisabeth Heisenberg, although subjective, allows to understand the scientist s behaviour face terrifying realities of his time. (N.C.)
Todorov, I
2005-01-01
A brief review of Heisenberg's life and work: participating in the youth movement in the aftermath of World War I, creating quantum mechanics, conflict with "deutsche Physik", involvement in "Hitler's Uranium Project", last illusions. Problems and dilemmas for scientists under a dictatorship - East and West.
Werner Heisenberg - Life and Work
2002-01-01
Werner Heisenberg (centre) with Wolfgang Pauli and Enrico Fermi, 1927. An exhibition on the life and work of Werner Heisenberg will be on display in the Main Building (Mezzanine) at CERN from 1 - 30 July*. German theoretical physicist Werner Karl Heisenberg (1901 - 1976) was one of the leading scientists of the 20th century. Nobel Prize in Physics in 1932, his most significant contribution was to the development of quantum mechanics. He is best known for his uncertainty principle, which restricts the accuracy with which some properties of atoms and particles can be determined simultaneously. Heisenberg was a keen supporter of CERN, and was as the first chairman of CERN's Scientific Policy Committee in October 1954. A related celebration will take place in the TH Amphitheatre (4/3-006), on Thursday 18 July at 16:00. After an introduction from the Director-General Luciano Maiani, his daughter, Barbara Blum, his last postgraduate, Helmut Rechenberg and Valentin Telegdi will evoke memories of the life and work ...
Werner Heisenberg - Life and Work
2002-01-01
Werner Heisenberg (centre) with Wolfgang Pauli (left) and Enrico Fermi on Lake Como, September 1927. An exhibition on the life and work of Werner Heisenberg will be on display in the Main Building (Mezzanine) at CERN from 1 - 23 July. The exhibition was produced by the University Archive of Leipzig University (Gerald Wiemers) and the Max-Planck-Institut für Physik in Munich (Helmut Rechenberg) to mark the centenary of Heisenberg's birth in 1901. German theoretical physicist Werner Karl Heisenberg (5 December 1901 - 1 February 1976) was one of the leading scientists of the 20th century. He carried out important work in nuclear and particle physics, but his most significant contribution was to the development of quantum mechanics. He is best known for his uncertainty principle, which restricts the accuracy with which some properties of atoms and particles - such as position and linear momentum - can be determined simultaneously. In 1932 he was awarded the Noble Prize in Physics 'for the creation of q...
Non-Hermitian Heisenberg representation
Znojil, Miloslav
2015-01-01
Roč. 379, č. 36 (2015), s. 2013-2017. ISSN 0375-9601 Institutional support: RVO:61389005 Keywords : quantum mechanics * Non-Hermitian representation of observables * Generalized Heisenberg equations Subject RIV: BE - Theoretical Physics Impact factor: 1.683, year: 2014
Spin-density functional for exchange anisotropic Heisenberg model
Prata, G.N.; Penteado, P.H.; Souza, F.C. [Departamento de Fisica e Informatica, Instituto de Fisica de Sao Carlos, Universidade de Sao Paulo, CP 369, Sao Carlos - SP (Brazil); Libero, Valter L., E-mail: valter@if.sc.usp.b [Departamento de Fisica e Informatica, Instituto de Fisica de Sao Carlos, Universidade de Sao Paulo, CP 369, Sao Carlos - SP (Brazil)
2009-10-15
Ground-state energies for antiferromagnetic Heisenberg models with exchange anisotropy are estimated by means of a local-spin approximation made in the context of the density functional theory. Correlation energy is obtained using the non-linear spin-wave theory for homogeneous systems from which the spin functional is built. Although applicable to chains of any size, the results are shown for small number of sites, to exhibit finite-size effects and allow comparison with exact-numerical data from direct diagonalization of small chains.
Spin-density functional for exchange anisotropic Heisenberg model
Ground-state energies for antiferromagnetic Heisenberg models with exchange anisotropy are estimated by means of a local-spin approximation made in the context of the density functional theory. Correlation energy is obtained using the non-linear spin-wave theory for homogeneous systems from which the spin functional is built. Although applicable to chains of any size, the results are shown for small number of sites, to exhibit finite-size effects and allow comparison with exact-numerical data from direct diagonalization of small chains.
Revisiting Riesz transforms on Heisenberg groups
Sanjay, P K
2011-01-01
We characterise higher order Riesz transforms on the Heisenberg group and also show that they satisfy dimension-free bounds under some assumptions on the multipliers. Using transfer- ence theorems, we deduce boundedness theorems for Riesz trans- forms on the reduced Heisenberg group and hence also for the Riesz transforms associated to multiple Hermite and Laguerre ex- pansions.
Heisenberg and the nazi uranium project
The author analyzes Heisenberg's scientific activities during Word War II and the background of his meeting with Bohr at Copenhagen in 1941. It is pointed out that, although Heisenberg was responsible for the Nazi uranium project, he did not actually take an active part in the research and manufacture of atomic bombs for the Nazi
Werner Karl Heisenberg (1901-1976)
The life's career of Werner Karl Heisenberg is described with emphasis on his creative development and cooperation with many other prominent physicists in the field of the quantum theory of atoms. In 1925, Heisenberg modified Bohr's quantum rule; in 1927 he formulated the uncertainty principle which puts some restrictions on the simultaneous determination of the position and momentum. In 1928, Heisenberg set up the quantum theory of ferromagnetism, which still underlies all theories of magnetic properties of substances. Soon after Chadwick's discovery of the neutron (1932), Heisenberg introduced the concept of the isospin - he interpreted the proton and the neutron as one particle (nucleon) in two charge states. Heisenberg's professional and pedagogical activities during and after the 2nd world war are also described. (Z.S.). 5 refs
胡仕刚; 刘云新; 吴笑峰; 唐志军; 李志明; 颜焕元; 陈增辉; 胡盼; 余意
2016-01-01
Lanthanide doped bifunctional materials are potentially important for developing multifunctional devices. Here, NaLuF4:Yb3+/Tm3+/Gd3+/Sm3+ optical-magnetic bifunctional microcrystals were successfully synthesized by hydrothermal method, which could emit ~480 nm blue light from the1G4→3H6 electronic transition and ~800 nm infrared light from the3H4→3H6electronic transition of Tm3+ ion, under the excitation of 980 nm infrared light. By doping Sm3+ ion into NaLuF4:Yb3+/Tm3+/Gd3+, the infrared emission peak centered at 800 nm would shift obviously to longer wavelength. This indicated that Sm3+ ion could efficiently tune the energy level gaps of Tm3+ ions in NaLuF4 host which was demonstrated based on the crystal field theory. In addition, these NaLuF4:Yb3+/Tm3+/Gd3+/Sm3+ microcrystals presented unique ferromagnetic property instead of usually reported paramagnetic prop-erty. Importantly, the ferromagnetic property decreased with increasing the concentration of Gd3+ ion. This was in good agreement with Swift’s theoretical investigation that the coexistence of light rare earth (Gd3+) and heavy rare earth (Yb3+/Tm3+) would lead to the anti-ferromagnetic coupling in the sub-lattices.
In the quest of materials with high temperature ferromagnetism and low temperature anti-ferromagnetism, we prepare Co3-xMnxTeO6; (0 ¯) structure for x ¯ structure for x ≥ 0.5. Further, it shows increase in both lattice parameters as well as average transition metal-oxygen (Co/Mn-O) bond lengths for x ≥ 0.5. Co and Mn K-edge XANES spectra reveal that both Co and Mn are in mixed oxidation state, Co2+/Mn2+ and Co3+/Mn3+. Relative ratios of Co3+/Co2+ and Mn3+/Mn2+ obtained using Linear combination fit decrease with increasing x (for x ≥ 0.5). These structural and spectroscopic evidences are used to provide possible interpretation of the observed paramagnetic to ferromagnetic transition at around 185 K followed by an enhanced antiferromagnetic transition ∼45 K for x = 0.5
Bond-Dilution-Induced Quantum Phase Transitions in Heisenberg Antiferromagnets
Yasuda, Chitoshi; Todo, Synge; Takayama, Hajime
2006-01-01
Bond-dilution effects on the ground state of the square-lattice antiferromagnetic Heisenberg model, consisting of coupled bond-alternating chains, are investigated by means of the quantum Monte Carlo simulation. It is found that, when the ground state of the non-diluted system is a non-magnetic state with a finite spin gap, a sufficiently weak bond dilution induces a disordered state with a mid gap in the original spin gap, and under a further stronger bond dilution an antiferromagnetic long-...
a Path-Integration Approach to the Correlators of XY Heisenberg Magnet and Random Walks
Bogoliubov, N. M.; Malyshev, C.
2008-11-01
The path integral approach is used for the calculation of the correlation functions of the XY Heisenberg chain. The obtained answers for the two-point correlators of the XX magnet are of the determinantal form and are interpreted in terms of the generating functions for the random turns vicious walkers.
A Unified Treatment for XXX-Heisenberg Model and Haldane-Shastry Model Using Shift Operators
Chen, J L; Xue, K; Zhao, X G; Chen, Jing-Ling; Ge, Mo-Lin; Xue, Kang; Zhao, Xian-Geng
2000-01-01
A unified treatment is developed for the XXX-Heisenberg model and a long-ranged interaction model (the $H_2$ in Haldane-Shastry model) from the point of view of shift operators (or raising and lowering operators), based on which the energy spectra of the spin-chain models are determined. Some physical discussions are also made.
Quantum states for Heisenberg limited interferometry
Uys, H
2007-01-01
The phase resolution of interferometers is limited by the so-called Heisenberg limit, which states that the optimum phase sensitivity is inversely proportional to the number of interfering particles $N$, a $1/\\sqrt{N}$ improvement over the standard quantum limit. We have used simulated annealing, a global optimization strategy, to systematically search for quantum interferometer input states that approach the Heisenberg limited uncertainty in estimates of the interferometer phase shift. We compare the performance of these states to that of other non-classical states already known to yield Heisenberg limited uncertainty.
Quantum states for Heisenberg limited interferometry
Uys, Hermann; Meystre, Pierre
2007-06-01
An important aspect of quantum metrology is the engineering of quantum states with which to achieve Heisenberg limited measurement precision. In this limit the measurement uncertainty is inversely proportional to the number of interfering particles, N, a 1/√N improvement over the standad quantum limit. We have used numerical global optimization strategies to systematically search for quantum interferometer input states that achieve Heisenberg limited uncertainty in estimates of the interferometer phase shift. We compare the performance of candidates so obtained with that of non-classical states already known to yield Heisenberg limited uncertainty.
Quantum states for Heisenberg-limited interferometry
Uys, H.; Meystre, P.
2007-07-01
The phase sensitivity of interferometers is limited by the so-called Heisenberg limit, which states that the optimum phase sensitivity is inversely proportional to the number of interfering particles N , a 1/N improvement over the standard quantum limit. We have used simulated annealing, a global optimization strategy, to systematically search for quantum interferometer input states that approach the Heisenberg-limited uncertainty in estimates of the interferometer phase shift. We compare the performance of these states to that of other nonclassical states already known to yield Heisenberg-limited uncertainty.
Quantum states for Heisenberg-limited interferometry
The phase sensitivity of interferometers is limited by the so-called Heisenberg limit, which states that the optimum phase sensitivity is inversely proportional to the number of interfering particles N, a 1/√(N) improvement over the standard quantum limit. We have used simulated annealing, a global optimization strategy, to systematically search for quantum interferometer input states that approach the Heisenberg-limited uncertainty in estimates of the interferometer phase shift. We compare the performance of these states to that of other nonclassical states already known to yield Heisenberg-limited uncertainty
Heisenberg's Uncertainty Relations and Quantum Optics
Agarwal, G. S.
2002-01-01
We present a brief review of the impact of the Heisenberg uncertainty relations on quantum optics. In particular we demonstrate how almost all coherent and nonclassical states of quantum optics can be derived from uncertainty relations.
Angular Operators Violating the Heisenberg Uncertainty Principle
Pereira, Tiago
2008-01-01
The description of a quantum system in terms of angle variables may violate Heisenberg uncertainty principle. The familiar case is the azimutal angle $\\phi$ and its canonical moment $L_z$. Although this problem was foreseen almost a century ago, up to the present days there are no criteria to precisely characterize the violation. In this paper, we present a theorem which provides necessary and sufficient conditions for the violation of the Heisenberg uncertainty principle. We illustrate our results with analytical examples.
Heisenberg Uncertainty Relation for Three Canonical Observables
Kechrimparis, Spiros; Weigert, Stefan
2014-01-01
Uncertainty relations provide fundamental limits on what can be said about the properties of quantum systems. For a quantum particle, the commutation relation of position and momentum observables entails Heisenberg's uncertainty relation. A third observable is presented which satisfies canonical commutation relations with both position and momentum. The resulting triple of pairwise canonical observables gives rise to a Heisenberg-type uncertainty relation for the product of three standard dev...
Pairwise entanglement and local polarization of Heisenberg model
2008-01-01
The characteristics of pairwise entanglement and local polarization (LP) are dis-cussed by studying the ground state (states) of the Heisenberg XX model. The re-sults show that: the ground state (states) is (are) composed of the micro states with the minimal polarization (0 for even qubit and 1/2 for odd qubit); LP and the prob-ability of the micro state have an intimate relation, i.e. the stronger the LP, the smaller the probability, and the same LP corresponds to the same probability; the pairwise entanglement of the ground state is the biggest in all eigenvectors. It is found that the pairwise entanglement is decreased by the state degeneracy and the system size. The concurrence approaches a fixed value of about 0.3412 (for odd-qubit chain) or 0.3491 (for even-qubit chain) if the qubit number is large enough.
Sigma Model Lagrangian for the Heisenberg Group
Baaquie, Belal E; Baaquie, Belal E.; Kean, Yim Kok
2005-01-01
We study the Lagrangian for a sigma model based on the non-compact Heisenberg group. A unique feature of this model -- unlike the case for compact Lie groups -- is that the definition of the Lagrangian has to be regulated since the trace over the Heisenberg group is otherwise divergent. The resulting theory is a real Lagrangian with a quartic interaction term. After a few non-trivial transformations, the Lagrangian is shown to be equivalent -- at the classical level -- to a complex cubic Lagrangian. A one loop computation shows that the quartic and cubic Lagrangians are equivalent at the quantum level as well. The complex Lagrangian is known to classically equivalent to the SU(2) sigma model, with the equivalence breaking down at the quantum level. An explanation of this well known results emerges from the properties of the Heisenberg sigma model.
Hilbert schemes of points and Heisenberg algebras
Let X[n] be the Hilbert scheme of n points on a smooth projective surface X over the complex numbers. In these lectures we describe the action of the Heisenberg algebra on the direct sum of the cohomologies of all the X[n], which has been constructed by Nakajima. In the second half of the lectures we study the relation of the Heisenberg algebra action and the ring structures of the cohomologies of the X[n], following recent work of Lehn. In particular we study the Chern and Segre classes of tautological vector bundles on the Hilbert schemes X[n]. (author)
More on generalized Heisenberg ferromagnet models
Oh, P; Oh, Phillial; Park, Q Han
1996-01-01
We generalize the integrable Heisenberg ferromagnet model according to each Hermitian symmetric spaces and address various new aspects of the generalized model. Using the first order formalism of generalized spins which are defined on the coadjoint orbits of arbitrary groups, we construct a Lagrangian of the generalized model from which we obtain the Hamiltonian structure explicitly in the case of CP(N-1) orbit. The gauge equivalence between the generalized Heisenberg ferromagnet and the nonlinear Schr\\"{o}dinger models is given. Using the equivalence, we find infinitely many conserved integrals of both models.
Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz
Samuel Belliard
2013-11-01
Full Text Available We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes the usual form of a product of operators acting on a particular vector except that the number of operators is equal to the length of the chain. We prove this result for the chains with small length. We obtain also an off-shell equation (i.e. satisfied without the Bethe equations formally similar to the ones obtained in the periodic case or with diagonal boundaries.
Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz
Belliard, Samuel; Crampé, Nicolas
2013-11-01
We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes the usual form of a product of operators acting on a particular vector except that the number of operators is equal to the length of the chain. We prove this result for the chains with small length. We obtain also an off-shell equation (i.e. satisfied without the Bethe equations) formally similar to the ones obtained in the periodic case or with diagonal boundaries.
Heisenberg XXX model with general boundaries: Eigenvectors from Algebraic Bethe ansatz
Belliard, S
2013-01-01
We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes the usual form of a product of operators acting on a particular vector except that the number of operators is equal to the length of the chain. We prove this result for the chains with small length. We obtain also an off-shell equation (i.e. satisfied without the Bethe equations) formally similar to the ones obtained in the periodic case or with diagonal boundaries.
Lindgård, Per-Anker
1984-01-01
The correlation theory is applied to a Heisenberg antiferromagnet in a magnetic field. Special cases covered are the ferromagnet and an anisotropic Heisenberg model. The theory includes selfconsistently correlation effects in static and dynamic properties. It is a generalization of the random......-phase approximation and is applicable to the quantum spin case for any dimension and temperature. The static susceptibilities and the excitation spectrum are calculated. Besides the spin-wave excitations a central peak is found which can be understood as coming from local longitudinal fluctuations. The results of the...... theory are exemplified by numerical calculations for the onedimensional S=1 quantum antiferromagnetic chain. Qualitative agreement is found with computer simulations on a classical chain....
Magnetic Properties of Quantum Ferrimagnetic Spin Chains
Yamamoto, Shoji
1998-01-01
Magnetic susceptibilities of spin-$(S,s)$ ferrimagnetic Heisenberg chains are numerically investigated. It is argued how the ferromagnetic and antiferromagnetic features of quantum ferrimagnets are exhibited as functions of $(S,s)$. Spin-$(S,s)$ ferrimagnetic chains behave like combinations of spin-$(S-s)$ ferromagnetic and spin-$(2s)$ antiferromagnetic chains provided $S=2s$.
Classifying tight Weyl-Heisenberg frames
Cazsazza, P.; Janssen, A. J. E. M.; Christensen, Ole
1999-01-01
A Weyl-Heisenberg frame for L^2(R) is a frame consisting of translates and modulates of a fixed function. In this paper we give necessary and sufficient conditions for this family to form a tight WH-frame. This allows us to write down explicitly all functions g for which all translates and...
Heisenberg algebra and a graphical calculus
Khovanov, Mikhail
2010-01-01
A new calculus of planar diagrams involving diagrammatics for biadjoint functors and degenerate affine Hecke algebras is introduced. The calculus leads to an additive monoidal category whose Grothendieck ring contains an integral form of the Heisenberg algebra in infinitely many variables. We construct bases of vector spaces of morphisms between products of generating objects in this category.
Classifying tight Weyl-Heisenberg frames
Cazsazza, P.; Janssen, A. J. E. M.; Christensen, Ole
A Weyl-Heisenberg frame for L^2(R) is a frame consisting of translates and modulates of a fixed function. In this paper we give necessary and sufficient conditions for this family to form a tight WH-frame. This allows us to write down explicitly all functions g for which all translates and modula...
Influence of Non-Uniform Magnetic Field on Quantum Teleportation in Heisenberg XY Model
SHAO Bin; YANG Tie-jian; ZHAO Yue-hong; ZOU Jian
2007-01-01
By considering the intrinsic decoherence, the validity of quantum teleportation of a two-qubit 1D Heisenberg XY chain in a non-uniform external magnetic field is studied. The fidelity as the measurement of a possible quantum teleportation is calculated and the effects of the non-uniform magnetic field and the intrinsic decoherence are discussed. It is found that anti-parallel magnetic field is more favorable for teleportation and the fidelity is suppressed by the intrinsic decoherence.
By using the modified spin-wave and gauge invariant methods, we show that at zero temperature in the presence of an inhomogeneous magnetic field with magnitude B gives rise to a persistent magnetization current around a mesoscopic antiferromagnetic Heisenberg spin ring with the DM (Dzyaloshinskii–Moriya) interaction. The results show that the persistent magnetization current is vanishing at large Ds/J (Ds is reduced DM interaction and J is nearest exchange coupling) with α>1 (α is a constant describing the energy gap of the spin system). The result also shows that under the homogeneous magnetic field there exists a non-zero spin current in the spin ring. - Highlights: • Persistent spin current is calculated in anti-ferromagnetic ring. • Persistent magnetization current is vanishing at large Ds/J. • Under homogeneous magnetic field there exists a non-zero spin current in the ring
Simulations of Information Transport in Spin Chains
Cappellaro, Paola; Ramanathan, Chandrasekhar; Cory, David G.
2007-01-01
Transport of quantum information in linear spin chains has been the subject of much theoretical work. Experimental studies by nuclear spin systems in solid-state by NMR (a natural implementation of such models) is complicated since the dipolar Hamiltonian is not solely comprised of nearest-neighbor XY-Heisenberg couplings. We present here a similarity transformation between the XY-Heisenberg Hamiltonian and the grade raising Hamiltonian, an interaction which is achievable with the collective ...
Bond diluted anisotropic quantum Heisenberg model
Effects of the bond dilution on the critical temperatures, phase diagrams and the magnetization behaviors of the isotropic and anisotropic quantum Heisenberg model have been investigated in detail. For the isotropic case, bond percolation threshold values have been determined for several numbers of two (2D) and three (3D) dimensional lattices. In order to investigate the effect of the anisotropy in the exchange interaction on the results obtained for the isotropic model, a detailed investigation has been made on a honeycomb lattice. Some interesting results, such as second order reentrant phenomena in the phase diagrams have been found. - Highlights: • Anisotropic quantum Heisenberg model with bond dilution investigated. • Bond percolation threshold values given for 2D and 3D lattices in isotropic case. • Phase diagrams and ground state magnetizations investigated in detail. • Variation of the bond percolation threshold values with anisotropy determined
Considerations on Bohr's, Heisenberg's and Schroedinger's philosophy
In denying that the words 'physical reality' are meaningful without reference to an experimental arrangement, Bohr renounces any knowledge of the 'thing-in-itself'. However, the relation of his epistemology to both idealism and positivism remains obscure. Heisenberg departs from Bohr in enunciating a metaphysical implication of quantum mechanics. Heisenberg asserts that there is an intermediate modality -potentiality- between logical possibility and existence. His attempts to explain the transition from potentiality to existence are not convincing. Schroedinger rejects Bohr's interpretation of quantum mechanics as a positivist exercise and seeks instead a realist interpretation. Nevertheless, the metaphysics of Schroedinger is fundamentally idealistic, maintaining that the material aspect of the world is composed of the same elements as mind, but in a different order
Bond diluted anisotropic quantum Heisenberg model
Akıncı, Ümit
2013-01-01
Effects of the bond dilution on the critical temperatures, phase diagrams and the magnetization behaviors of the isotropic and anisotropic quantum Heisenberg model have been investigated in detail. For the isotropic case, bond percolation threshold values have been determined for several numbers of two (2D) and three (3D) dimensional lattices. In order to investigate the effect of the anisotropy in the exchange interaction on the results obtained for the isotropic model, a detailed investigat...
Perturbations of Weyl-Heisenberg frames
Casazza, Peter G.; Christensen, Ole; Lammers, Mark C.
2000-01-01
We develop a usable perturbation theory for Weyl-Heisenberg frames. In particular, we prove that if $(E_{mb}T_{na}g)_{m,n\\inmathbb Z}$ is a WH-frame and $h$ is a function which is close to $g$ in the Wiener Amalgam space norm, then $(E_{mb}T_{na}h)_{m,n\\in \\mathbb Z}$ is also a WH-frame.
Controllable entanglement sudden birth of Heisenberg spins
ZHENG Qiang; ZHI Qi-Jun; ZHANG Xiao-ping; REN Zhong-Zhou
2011-01-01
We investigate the Entanglement Sudden Birth (ESB) of two Heisenberg spins A and B. The third controller, qutrit C is introduced, which only has the Dzyaloshinskii-Moriya (DM) spin-orbit interaction with qubit B. We find that the DM interaction is necessary to induce the Entanglement Sudden Birth of the system qubits A and B, and the initial states of the system qubits and the qurit C are also important to control its Entanglement Sudden Birth.
Heisenberg Uncertainty Principle in high school teaching
Pinto, Albino Rafael Mesquita; Marques, L.; Ramos, Marta M. D.
2013-01-01
In Portuguese high school curricula concepts of quantum physics are taught in the discipline of physics in the 12th year of education. These concepts underlie the functioning of modern nano devices and nanotechnologies, but are difficult to understand by the students of this level of teaching, thus making it necessary the integration of new strategies to facilitate teaching-learning process. In this we show the activities we developed to illustrate the Heisenberg uncertainty relations, ...
Ordered Phase in the Fermionized Heisenberg Antiferromagnet
Azakov, S.; Dilaver, M.; Oztas, A. M.
1999-01-01
Thermal properties of the ordered phase of the spin 1/2 isotropic Heisenberg Antiferromagnet on a d-dimensional hypercubical lattice are studied within the fermionic representation when the constraint of single occupancy condition is taken into account by the method suggested by Popov and Fedotov. Using saddle point approximation in path integral approach we discuss not only the leading order but also the fluctuations around the saddle point at one-loop level. The influence of taking into acc...
Quantum kinetic Heisenberg models: a unique dynamics
We suggest that the dynamics Glauber embodied in his kinetic Ising model can be introduced similarly and in an apparently unique way, into the quantum statistical mechanics of the quantum-integrable models like the Heisenberg, sine-Gordon and Massive Thirring models. The latter may suggest an extension of the theory to unique kinetic Ising models in two dimensions. The kinetic repulsive bose gas which is studied in detail in the steady state seems to be a solvable kinetic model. (author)
Local Spin Correlations in Heisenberg Antiferromagnets
Weihong, Zheng; Oitmaa, J.
2000-01-01
We use linked cluster series expansion methods to estimate the values of various short distance correlation functions in $S=1/2$ Heisenberg antiferromagnets at T=0, for dimension $d=1,2,3$. The method incorporates the possibility of spontaneous symmetry breaking, which is manifest in $d=2,3$. The results are important in providing a test for approximate theories of the antiferromagnetic ground state.
Minimal surfaces in the Heisenberg group
Pauls, Scott D.
2001-01-01
We investigate the minimal surface problem in the three dimensional Heisenberg group, H, equipped with its standard Carnot-Caratheodory metric. Using a particular surface measure, we characterize minimal surfaces in terms of a sub-elliptic partial differential equation and prove an existence result for the Plateau problem in this setting. Further, we provide a link between our minimal surfaces and Riemannian constant mean curvature surfaces in H equipped with different Riemannian metrics appr...
Watson-Crick pairing, the Heisenberg group and Milnor invariants
Gadgil, Siddhartha
2008-01-01
We study the secondary structure of RNA determined by Watson-Crick pairing without pseudo-knots using Milnor invariants of links. We focus on the first non-trivial invariant, which we call the Heisenberg invariant. The Heisenberg invariant, which is an integer, can be interpreted in terms of the Heisenberg group as well as in terms of lattice paths. We show that the Heisenberg invariant gives a lower bound on the number of unpaired bases in an RNA secondary structure. We also show that the Heisenberg invariant can predict \\emph{allosteric structures} for RNA. Namely, if the Heisenberg invariant is large, then there are widely separated local maxima (i.e., allosteric structures) for the number of Watson-Crick pairs found.
Heisenberg, his wife s account; Heisenberg, le temoignage de sa femme
Heisenberg, E.
1990-12-31
A wife tells about her husband life, Werner Heisenberg, Physics Nobel Price in 1932. After a happy childhood, this brilliant student was Albert Einstein, Niels Bohr, Arnold Sommerfeld s student. But at the nazism time, the great physician refused to leave his country, guaranteeing the Hitler regime and taking part in effort of war, that is to say the run to the bomb. The account of Elisabeth Heisenberg, although subjective, allows to understand the scientist s behaviour face terrifying realities of his time. (N.C.).
Quantum phase transition in dimerised spin-1/2 chains
Das, Aparajita; Bhadra, Sreeparna; Saha, Sonali
2015-11-01
Quantum phase transition in dimerised antiferromagnetic Heisenberg spin chain has been studied. A staircase structure in the variation of concurrence within strongly coupled pairs with that of external magnetic field has been observed indicating multiple critical (or critical like) points. Emergence of entanglement due to external magnetic field or magnetic entanglement is observed for weakly coupled spin pairs too in the same dimer chain. Though closed dimerised isotropic XXX Heisenberg chains with different dimer strengths were mainly explored, analogous studies on open chains as well as closed anisotropic (XX interaction) chains with tilted external magnetic field have also been studied.
ZHENG Qiang; ZHI Qi-Jun; ZHANG Xiao-Ping; REN Zhong-Zhou
2011-01-01
We investigate the Entanglement Sudden Birth （ESB） of two Heisenberg spins A and B. The third controller, qutrit C is introduced, which only has the Dzyaloshinskii-Moriya （DM） spin-orbit interaction with qubit B. We find that the DM interaction is necessa
Classical and quantum anisotropic Heisenberg antiferromagnets
W. Selke
2009-01-01
Full Text Available We study classical and quantum Heisenberg antiferromagnets with exchange anisotropy of XXZ-type and crystal field single-ion terms of quadratic and quartic form in a field. The magnets display a variety of phases, including the spin-flop (or, in the quantum case, spin-liquid and biconical (corresponding, in the quantum lattice gas description, to supersolid phases. Applying ground-state considerations, Monte Carlo and density matrix renormalization group methods, the impact of quantum effects and lattice dimension is analysed. Interesting critical and multicritical behaviour may occur at quantum and thermal phase transitions.
Thermodynamic properties of Heisenberg magnetic systems
In this paper, we present a comprehensive investigation of the effects of the transverse correlation function (TCF) on the thermodynamic properties of Heisenberg antiferromagnetic (AFM) and ferromagnetic (FM) systems with cubic lattices. The TCF of an FM system is positive and increases with temperature, while that of an AFM system is negative and decreases with temperature. The TCF lowers internal energy, entropy and specific heat. It always raises the free energy of an FM system but raises that of an AFM system only above a specific temperature when the spin quantum number is S ≥ 1. Comparisons between the effects of the TCFs on the FM and AFM systems are made where possible
Heisenberg's Uncertainty : an Ill-Defined Notion ?
Rosinger, Elemer Elad
2012-01-01
The often cited book [11] of Asher Peres presents Quantum Mechanics without the use of the Heisenberg Uncertainty Principle, a principle which it calls an "ill-defined notion". There is, however, no argument in this regard in the mentioned book, or comment related to the fact that its use in the realms of quanta is not necessary, let alone, unavoidable. A possible comment in this respect is presented here. And it is related to certain simple, purely logical facts in axiomatic theories, facts ...
Heisenberg Model in a Rotating Magnetic Field
LIN Qiong-Gui
2005-01-01
We study the Heisenberg model under the influence of a rotating magnetic field. By using a time-dependent unitary transformation, the time evolution operator for the Schrodinger equation is obtained, which involves no chronological product. The spin vectors (mean values of the spin operators) are obtained as explicit functions of time in the most general case. A series of cyclic solutions are presented. The nonadiabatic geometric phases of these cyclic solutions are calculated, and are expressed in terms of the solid angle subtended by the closed trace of the total spin vector, as well as in terms of those of the individual spins.
Heisenberg-Euler Effective Lagrangians : Basics and Extensions
Dunne, Gerald V.
2004-01-01
I present a pedagogical review of Heisenberg-Euler effective Lagrangians, beginning with the original work of Heisenberg and Euler, and Weisskopf, for the one loop effective action of quantum electrodynamics in a constant electromagnetic background field, and then summarizing some of the important applications and generalizations to inhomogeneous background fields, nonabelian backgrounds, and higher loop effective Lagrangians.
Nonlinear Liouville Theorem in the Quaternionic Heisenberg Group
YANG Qiao-hua; ZHU Fu-liu
2005-01-01
This paper deals with the problem of the type△Hf+fp =0 in quaternionic Heisenberg group, where △H isthe quaternionic Heisenberg Laplacian. It is proved that, under suitable conditions on p and f, the only solution of △Hf+fp =0 is f≡0.
XYZ Quantum Heisenberg Models with p-Orbital Bosons
Pinheiro, Fernanda; Bruun, Georg; Martikainen, Jani-Petri;
2013-01-01
We demonstrate how the spin-1/2 XYZ quantum Heisenberg model can be realized with bosonic atoms loaded in the p band of an optical lattice in the Mott regime. The combination of Bose statistics and the symmetry of the p-orbital wave functions leads to a nonintegrable Heisenberg model with...
Proof of Heisenberg's Error-Disturbance Relation
Busch, Paul; Lahti, Pekka; Werner, Reinhard F.
2013-10-01
While the slogan “no measurement without disturbance” has established itself under the name of the Heisenberg effect in the consciousness of the scientifically interested public, a precise statement of this fundamental feature of the quantum world has remained elusive, and serious attempts at rigorous formulations of it as a consequence of quantum theory have led to seemingly conflicting preliminary results. Here we show that despite recent claims to the contrary [L. Rozema et al, Phys. Rev. Lett. 109, 100404 (2012)], Heisenberg-type inequalities can be proven that describe a tradeoff between the precision of a position measurement and the necessary resulting disturbance of momentum (and vice versa). More generally, these inequalities are instances of an uncertainty relation for the imprecisions of any joint measurement of position and momentum. Measures of error and disturbance are here defined as figures of merit characteristic of measuring devices. As such they are state independent, each giving worst-case estimates across all states, in contrast to previous work that is concerned with the relationship between error and disturbance in an individual state.
Heisenberg and the framework of science policy
In the decades after 1945, new structures were created for science policy in the Federal Republic. To the establishment of the postwar framework Heisenberg contributed as much as any other figure. This was true even though, on the whole, he took no great pleasure in the venture, nor was he always particularly adept at it. His conceptions revolved around certain key notions: autonomy and centralization, elite advisory bodies and relationships of trust, modernization and international standards. These show up at many levels of his activity, from the Max Planck Society to national and international advisory committees to the Humboldt Foundation itself. His opinions were shaped by encounters in the Federal Republic, but they also grew out of his experience of the Third Reich. At a moment like the present, when the postwar settlement is under review, it is interesting to reflect on the inherited system: on the extent to which it reflects the situation of the postwar decades and the intuitions of those who, like Heisenberg, created it. (orig.)
Monte Carlo study of four-spinon dynamic structure function in antiferromagnetic Heisenberg model
Using Monte Carlo integration methods, we describe the behavior of the exact four-s pinon dynamic structure function S4 in the antiferromagnetic spin 1/2 Heisenberg quantum spin chain as a function of the neutron energy ω and momentum transfer k. We also determine the fourspinon continuum, the extent of the region in the (k, ω) plane outside which S4 is identically zero. In each case, the behavior of S4 is shown to be consistent with the four-spinon continuum and compared to the one of the exact two-spinon dynamic structure function S2. Overall shape similarity is noted. (author)
Heisenberg antiferromagnet on the Husimi lattice
Liao, H. J.; Xie, Z. Y.; Chen, J.; Han, X. J.; Xie, H. D.; Normand, B.; Xiang, T.
2016-02-01
We perform a systematic study of the antiferromagnetic Heisenberg model on the Husimi lattice using numerical tensor-network methods based on projected entangled simplex states. The nature of the ground state varies strongly with the spin quantum number S . For S =1/2 , it is an algebraic (gapless) quantum spin liquid. For S =1 , it is a gapped, nonmagnetic state with spontaneous breaking of triangle symmetry (a trimerized simplex-solid state). For S =2 , it is a simplex-solid state with a spin gap and no symmetry breaking; both integer-spin simplex-solid states are characterized by specific degeneracies in the entanglement spectrum. For S =3/2 , and indeed for all spin values S ≥5/2 , the ground states have 120∘ antiferromagnetic order. In a finite magnetic field, we find that, irrespective of the value of S , there is always a plateau in the magnetization at m =1/3 .
Open timelike curves violate Heisenberg's uncertainty principle
Pienaar, J L; Ralph, T C
2012-01-01
Toy models for quantum evolution in the presence of closed timelike curves (CTCs) have gained attention in the recent literature due to the strange effects they predict. The circuits that give rise to these effects appear quite abstract and contrived, as they require non-trivial interactions between the future and past which lead to infinitely recursive equations. We consider the special case in which there is no interaction inside the CTC, referred to as an open timelike curve (OTC), for which the only local effect is to increase the time elapsed by a clock carried by the system. Remarkably, circuits with access to OTCs are shown to violate Heisenberg's uncertainty principle, allowing perfect state discrimination and perfect cloning of coherent states. The model is extended to wave-packets and smoothly recovers standard quantum mechanics in an appropriate physical limit. The analogy with general relativistic time-dilation suggests that OTCs provide a novel alternative to existing proposals for the behaviour ...
Polarizability tensor and Kramers-Heisenberg induction
A general expression for the semiclassical, nonrelativistic linear polarizability of an arbitrary volume element V has been derived in the long wavelength approximation. The derivation starts from the expectation value of the dipole strength, as in the original Kramers-Heisenberg paper about optical scattering by atoms. The main requirements underlying the present approach are a separate non-Hermitian part of the Hamiltonian and a frequency dependent damping, which is zero for the static case. Resonant and antiresonant exponentials are both found to be necessary to obtain a proper static response. It is concluded that even parity for the damping has to be preferred from the theoretical point of view, although odd and asymmetric parity yield virtually the same polarizability. The electromagnetic response can still be written in terms of a single complex frequency, in agreement with the requirements of electrodynamics. The resulting expression is suited for the treatment of nonisotropic systems
Generalized Coherent States for Polynomial Weyl-Heisenberg Algebras
Kibler, Maurice Robert; Daoud, Mohammed
2011-01-01
It is the aim of this paper to show how to construct Perelomov and Barut-Girardello coherent states for a polynomial Weyl-Heisenberg algebra. This algebra depends on r parameters. For some special values of the parameter corresponding to r = 1, the algebra covers the cases of the su(1,1) algebra, the su(2) algebra and the ordinary Weyl-Heisenberg or oscillator algebra. For r arbitrary, the generalized Weyl-Heisenberg algebra admits finite or infinite-dimensional representations depending on t...
Classifying characteristic functions giving Weyl-Heisenberg frames
Casazza, P. G.; Lammers, M. C.
2000-01-01
We examine the question of which characteristic functions yield Weyl-Heisenberg frames for various values of the parameters. We also give numerous applications of frames of characteristic functions to the general case (g,a,b).
Beyond Uncertainty Heisenberg, Quantum Physics, and The Bomb
Cassidy, David C
2010-01-01
Award winning biographer revisits the controversial life of this well known German physicist to shed new light on troubling questions. What can we learn about the relationship of scientific research to state power from Heisenberg's role in Nazi Germany?
Some remarks on densities in the Heisenberg group
Magnani, Valentino
2015-01-01
We observe that upper densities and spherical Federer densities may differ on all two dimensional surfaces of the sub-Riemannian Heisenberg group. This provides an entire class of intrinsic rectifiable sets having upper density strictly less than one.
An improved Hardy type inequality on Heisenberg group
Xiao Ying-Xiong
2011-01-01
Full Text Available Abstract Motivated by the work of Ghoussoub and Moradifam, we prove some improved Hardy inequalities on the Heisenberg group ℍ n via Bessel function. Mathematics Subject Classification (2000: Primary 26D10
Whittaker modules for the twisted Heisenberg-Virasoro algebra
We define Whittaker modules for the twisted Heisenberg-Virasoro algebra and obtain several results from the classical setting, including a classification of simple Whittaker modules by central characters.
Heisenberg Groups and their Automorphisms over Algebras with Central Involution
Johnson, Robert W.
2015-08-01
Heisenberg groups over algebras with central involution and their automorphism groups are constructed. The complex quaternion group algebra over a prime field is used as an example. Its subspaces provide finite models for each of the real and complex quadratic spaces with dimension 4 or less. A model for the representations of these Heisenberg groups and automorphism groups is constructed. A pseudo-differential operator enables a parallel treatment of spaces defined over finite and real fields.
Magnetic Properties of Heisenberg Thin Films in an External Field
CHEN Hong; ZHANG Jing
2004-01-01
The magnetic properties of Heisenberg ferromagnetic films in an external magnetic field are investigated by means of the variational cumulant expansion (VCE). The magnetization can be in principle calculated analytically as the function of the temperature and the number of atomic layers in the film to an arbitrary order of accuracy in the VCE. We calculate the spontaneous magnetization and coercivity to the third order for spin-1/2 Heisenberg films with simple cubic lattices by using a graphic technique.
On the rational relationship between Heisenberg principle and general relativity
Xiao, Jianhua
2006-01-01
The research shows that the Heisenberg principle is the logic results of general relativity principle. If inertia coordinator system is used, the general relativity will logically be derived from the Heisenberg principle. The intrinsic relation between the quantum mechanics and general relativity is broken by introducing pure-imaginary time to explain the Lorentz transformation. Therefore, this research shows a way to establish an unified field theory of physics
The Virtually Cyclic Classifying Space of the Heisenberg Group
Manion, Andrew; Pham, Lisa; Poelhuis, Jonathan
2008-01-01
We are interested in the relationship between the virtual cohomological dimension (or vcd) of a discrete group Gamma and the smallest possible dimension of a model for the classifying space of Gamma relative to its family of virtually cyclic subgroups. In this paper we construct a model for the virtually cyclic classifying space of the Heisenberg group. This model has dimension 3, which equals the vcd of the Heisenberg group. We also prove that there exists no model of dimension less than 3.
Impure Heisenberg systems with biquadratic interactions
Chakraborty, K. G.
1980-08-01
The purpose of the present paper is to study an impure Heisenberg ferromagnet governed by the Hamiltonian H=-Ji,Δ[S-->i.S-->i+Δ+α(S-->i.S-->i+Δ)2]-2J0Δ[S-->0.S-->Δ+α0(S-->0.S-->Δ)2], where J is the host-host bilinear exchange constant, 2(J+J0) is the host-impurity bilinear exchange constant, α and α0 being the corresponding biquadratic coupling parameters, and Δ, a nearest-neighbor vector. S--> and S-->0 are the host and the impurity spins, respectively. Through utilization of the Dyson transformation, it is shown that at low temperatures the effect of the biquadratic terms is simply to renormalize the bilinear exchange constants J and J0 by 1+2αS(S-1) and 1+α0(2SS0-S-S0), respectively. Some qualitative discussions on the scattering processes are presented. The method of Green's function is then employed to discuss the criteria for the existence of localized modes in the system. The situations appearing in KMnF3, RbMnF3, KNiF3, and MnF2 doped by impurities are critically examined. Some numerical estimates of the biquadratic parameters α and α0 are also made which are found to agree satisfactorily with those obtained by previous authors.
Nonlinear phonon interferometry at the Heisenberg limit
Cheung, Hil F. H.; Patil, Yogesh Sharad; Chang, Laura; Chakram, Srivatsan; Vengalattore, Mukund
2016-05-01
Interferometers operating at or close to quantum limits of precision have found wide application in tabletop searches for physics beyond the standard model, the study of fundamental forces and symmetries of nature and foundational tests of quantum mechanics. The limits imposed by quantum fluctuations and measurement backaction on conventional interferometers (δϕ 1 /√{ N}) have spurred the development of schemes to circumvent these limits through quantum interference, multiparticle interactions and entanglement. Here, we realize a prominent example of such schemes, the so-called SU(1,1) interferometer, in a fundamentally new platform in which the interfering arms are distinct flexural modes of a millimeter-scale mechanical resonator. We realize up to 15.4(3) dB of noise squeezing and demonstrate the Heisenberg scaling of interferometric sensitivity (δϕ 1 / N), corresponding to a 6-fold improvement in measurement precision over a conventional interferometer. We describe how our work extends the optomechanical toolbox and how it presents new avenues for studies of optomechanical sensing and studies of nonequilibrium dynamics of multimode optomechanical systems. This work was supported by the DARPA QuASAR program through a grant from the ARO, the ARO MURI on non-equilibrium manybody dynamics and an NSF INSPIRE award.
Linear dependencies in Weyl-Heisenberg orbits
Dang, Hoan Bui; Blanchfield, Kate; Bengtsson, Ingemar; Appleby, D. M.
2013-11-01
Five years ago, Lane Hughston showed that some of the symmetric informationally complete positive operator valued measures (SICs) in dimension 3 coincide with the Hesse configuration (a structure well known to algebraic geometers, which arises from the torsion points of a certain elliptic curve). This connection with elliptic curves is signalled by the presence of linear dependencies among the SIC vectors. Here we look for analogous connections between SICs and algebraic geometry by performing computer searches for linear dependencies in higher dimensional SICs. We prove that linear dependencies will always emerge in Weyl-Heisenberg orbits when the fiducial vector lies in a certain subspace of an order 3 unitary matrix. This includes SICs when the dimension is divisible by 3 or equal to 8 mod 9. We examine the linear dependencies in dimension 6 in detail and show that smaller dimensional SICs are contained within this structure, potentially impacting the SIC existence problem. We extend our results to look for linear dependencies in orbits when the fiducial vector lies in an eigenspace of other elements of the Clifford group that are not order 3. Finally, we align our work with recent studies on representations of the Clifford group.
Non self-conjugate strings, singular strings and rigged configurations in the Heisenberg model
We observe a different type of complex solutions in the isotropic spin-1/2 Heisenberg chain starting from N = 12, where the central rapidity of some of the odd-length strings becomes complex so that not all the strings self-conjugate individually. We show that there are at most (N − 2)/2 singular solutions for M = 4, M = 5 down-spins and at most (N2 − 6N + 8)/8 singular solutions for M = 6, M = 7 down-spins in an even-length chain with N ⩾ 2M. Correspondence of the non self-conjugate string solutions and the singular string solutions to the rigged configurations has also been shown. (paper)
Microscopic Origin of Heisenberg and Non-Heisenberg Exchange Interactions in Ferromagnetic bcc Fe.
Kvashnin, Y O; Cardias, R; Szilva, A; Di Marco, I; Katsnelson, M I; Lichtenstein, A I; Nordström, L; Klautau, A B; Eriksson, O
2016-05-27
By means of first principles calculations, we investigate the nature of exchange coupling in ferromagnetic bcc Fe on a microscopic level. Analyzing the basic electronic structure reveals a drastic difference between the 3d orbitals of E_{g} and T_{2g} symmetries. The latter ones define the shape of the Fermi surface, while the former ones form weakly interacting impurity levels. We demonstrate that, as a result of this, in Fe the T_{2g} orbitals participate in exchange interactions, which are only weakly dependent on the configuration of the spin moments and thus can be classified as Heisenberg-like. These couplings are shown to be driven by Fermi surface nesting. In contrast, for the E_{g} states, the Heisenberg picture breaks down since the corresponding contribution to the exchange interactions is shown to strongly depend on the reference state they are extracted from. Our analysis of the nearest-neighbor coupling indicates that the interactions among E_{g} states are mainly proportional to the corresponding hopping integral and thus can be attributed to be of double-exchange origin. By making a comparison to other magnetic transition metals, we put the results of bcc Fe into context and argue that iron has a unique behavior when it comes to magnetic exchange interactions. PMID:27284671
Heisenberg lecture: Supersymmetry in the spectra of atomic nuclei
Talk given at the Symposium: 'Werner Heisenberg und die Wissenschaft, das Denken und die Kunst', Alexander von Humboldt Club, Bucharest, October 16 - 17, 2001, Goethe-Institut, Bucharest, Romania. This Symposium of the Humboldt Club in Bucharest was dedicated to the work of Werner Heisenberg. With the occasion of the hundredth anniversary of his birthday the aim was to recall the impact of Heisenberg's work not only on physics and related fields but also on philosophy and on our present understanding of science. Werner Heisenberg discovered and formulated the laws of quantum physics, the concepts and the tools one uses at present. These discoveries resulted from his ambitious goal to reveal the fundamental laws of physics and to understand these laws within the logical and structural aspects they imply for the understanding of nature and of thinking. In this way he was aware of the potential of this fundamental new approach and applied the concept of quantum phenomena to physics, chemistry, biology, and to logical-philosophical questions. Being invited here as first speaker of this Symposium the author considered as appropriate, first to recall a few dates out of his vita and essentials of his work, and then to address to a timely subject, which is, hopefully, related to the work of Werner Heisenberg. (author)
A superfluid spin phase in ferromagnetic chains
I show that for a spin-1/2 ferromagnetic Heisenberg chain, a new spontaneously broken symmetry state with no spontaneous magnetization, degenerate to the ferromagnetically ordered ground state exists in a generalized mean field theory. It has off-diagonal long-range order. Consequently a 3-dimensional system of weakly coupled ferromagnetic chains can have this new order at low temperatures. Some interesting experimentally observable predictions are made. (author)
Trudinger-Moser inequalities on the entire Heisenberg group
Yang, Yunyan
2012-01-01
Continuing our previous work (Cohn, Lam, Lu, Yang, Nonlinear Analysis (2011), doi: 10.1016 /j.na.2011.09.053), we obtain a class of Trudinger-Moser inequalities on the entire Heisenberg group, which indicate what the best constants are. All the existing proofs of similar inequalities on unbounded domain of the Euclidean space or the Heisenberg group are based on rearrangement argument. In this note, we propose a new approach to solve this problem. Specifically we get the global Trudinger-Moser inequality by gluing local estimates with the help of cut-off functions. Our method still works for similar problems when the Heisenberg group is replaced by the Eclidean space or complete noncompact Riemannian manifolds.
Heisenberg scaling of imaging resolution by coherent enhancement
McConnell, Robert; Yoder, Theodore J; Bruzewicz, Colin D; Chuang, Isaac L; Chiaverini, John; Sage, Jeremy M
2016-01-01
Classical imaging works by scattering photons from an object to be imaged, and achieves resolution scaling as $1/\\sqrt{t}$, with $t$ the imaging time. By contrast, the laws of quantum mechanics allow one to utilize quantum coherence to obtain imaging resolution that can scale as quickly as $1/t$ -- the so-called "Heisenberg limit." However, ambiguities in the obtained signal often preclude taking full advantage of this quantum enhancement, while imaging techniques designed to be unambiguous often lose this optimal Heisenberg scaling. Here, we demonstrate an imaging technique which combines unambiguous detection of the target with Heisenberg scaling of the resolution. We also demonstrate a binary search algorithm which can efficiently locate a coherent target using the technique, resolving a target trapped ion to within 3% of the $1/e^2$ diameter of the excitation beam.
Heisenberg in the atomic age science and the public sphere
Carson, Cathryn
2010-01-01
The end of the Second World War opened a new era for science in public life. Heisenberg in the Atomic Age explores the transformations of science's public presence in the postwar Federal Republic of Germany. It shows how Heisenberg's philosophical commentaries, circulating in the mass media, secured his role as science's public philosopher, and it reflects on his policy engagements and public political stands, which helped redefine the relationship between science and the state. With deep archival grounding, the book tracks Heisenberg's interactions with intellectuals from Heidegger to Habermas and political leaders from Adenauer to Brandt. It also traces his evolving statements about his wartime research on nuclear fission for the National Socialist regime. Working between the history of science and German history, the book's central theme is the place of scientific rationality in public life - after the atomic bomb, in the wake of the Third Reich.
Modified Heisenberg model for the zig-zag structure in multiferroic RMn2O5
The class of RMn2O5 (R = Ho, Tb, Y, Eu) compounds offers multiferroic properties where the refined magnetic zig-zag order breaks the inversion symmetry. Varying the temperature, the system undergoes a magnetic and a subsequent ferroelectric phase transition where the ferroelectricity is magnetically induced. We propose a modified anisotropic Heisenberg model that can be used as a tractable analytical model studying the properties of those antiferromagnetic zig-zag spin chains. Based on a finite temperature Green's function method, it is shown that the polarization is induced solely by different exchange couplings of the two different Mn4+ and Mn3+ magnetic ions. We calculate the excitation energy of the spin system for finite temperatures, which for its part determines the temperature dependent magnetization and polarization. The ferroelectric phase transition is manifested as a kink in the excitation energy. The variation of the polarization by an external magnetic field depends strongly on the direction of that field. Whereas, the polarization in b-direction increases with an external magnetic field as well in b-direction it can be switched for strong fields in a-direction. The results based on that modified Heisenberg model are in qualitative agreement with experimental data
A survey of algebraic actions of the discrete Heisenberg group
Lind, D.; Schmidt, K.
2015-08-01
The study of actions of countable groups by automorphisms of compact Abelian groups has recently undergone intensive development, revealing deep connections with operator algebras and other areas. The discrete Heisenberg group is the simplest non-commutative example, where dynamical phenomena related to its non-commutativity already illustrate many of these connections. The explicit structure of this group means that these phenomena have concrete descriptions, which are not only instances of the general theory but are also testing grounds for further work. This paper surveys what is known about such actions of the discrete Heisenberg group, providing numerous examples and emphasizing many of the open problems that remain. Bibliography: 71 titles.
The Finite Heisenberg-Weyl Groups in Radar and Communications
Calderbank AR
2006-01-01
Full Text Available We investigate the theory of the finite Heisenberg-Weyl group in relation to the development of adaptive radar and to the construction of spreading sequences and error-correcting codes in communications. We contend that this group can form the basis for the representation of the radar environment in terms of operators on the space of waveforms. We also demonstrate, following recent developments in the theory of error-correcting codes, that the finite Heisenberg-Weyl groups provide a unified basis for the construction of useful waveforms/sequences for radar, communications, and the theory of error-correcting codes.
Heisenberg-Weyl algebra revisited: combinatorics of words and paths
The Heisenberg-Weyl algebra, which underlies virtually all physical representations of quantum theory, is considered from the combinatorial point of view. We provide a concrete model of the algebra in terms of paths on a lattice with some decomposition rules. We also discuss the rook problem on the associated Ferrers board; this is related to the calculus in the normally ordered basis. From this starting point we explore combinatorial underpinning of the Heisenberg-Weyl algebra, which offers novel perspectives, methods and applications
Quantum crystals and spin chains
Dijkgraaf, Robbert [KdV Institute for Mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam (Netherlands); Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands); Orlando, Domenico [Institut de Physique, Universite de Neuchatel, Rue Breguet 1, CH-2000 Neuchatel (Switzerland); Reffert, Susanne [Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands)], E-mail: sreffert@gmail.com
2009-04-21
In this article, we discuss the quantum version of the melting crystal corner in one, two, and three dimensions, generalizing the treatment for the quantum dimer model. Using a mapping to spin chains we find that the two-dimensional case (growth of random partitions) is integrable and leads directly to the Hamiltonian of the Heisenberg XXZ ferromagnet. The three-dimensional case of the melting crystal corner is described in terms of a system of coupled XXZ spin chains. We give a conjecture for its mass gap and analyze the system numerically.
Deformed Heisenberg algebra, fractional spin fields and supersymmetry without fermions
Plyushchay, M S
1994-01-01
Within a group-theoretical approach to the description of (2+1)-dimensional anyons, the minimal covariant set of linear differential equations is constructed for the fractional spin fields with the help of the deformed Heisenberg algebra (DHA), [a^{-},a^{+}]=1+\
On the magnetism of Heisenberg double-layer antiferromagnets
The author investigates the sublattice magnetization and the susceptibility of the double-layer Heisenberg antiferromagnet K3M2F7 by employing the techniques of elastic and quasi-elastic critical magnetic scattering of neutrons. (G.T.H.)
The Bohr-Heisenberg correspondence principle viewed from phase space
Dahl, Jens Peder
Phase-space representations play an increasingly important role in several branches of physics. Here, we review the author's studies of the Bohr-Heisenberg correspondence principle within the Weyl-Wigner phase-space representation. The analysis leads to refined correspondence rules that can be...
Direct Calculation of Thermodynamic Quantities for Heisenberg Model
Kato, Go; Wadati, Miki
2002-01-01
The XXX Heisenberg model is studied at finite temperature. The free energy is derived without recourse to Thermal Bethe Ansatz method and Quantum Transfer Matrix method. The result perfectly agrees with the free energy derived by Thermal Bethe Ansatz method. An explicit expression of the cluster expansion coefficient in arbitrary order is presented for the first time.
IMPROVED GAGLIARDO-NIRENBERG INEQUALITIES ON HEISENBERG TYPE GROUPS
Luo Guangzhou
2011-01-01
Motivated by the idea of M.Ledoux who brings out the connection between Sobolev embeddings and heat kernel bounds,we prove an analogous result for Kohn's sub-Laplacian on the Heisenberg type groups.The main result includes features of an inequality of either Sobolev or Galiardo-Nirenberg type.
Effect of the site dilution on spin transport in the two-dimensional biquadratic Heisenberg model
Lima, L. S.
2016-05-01
We use the SU(3) Schwinger's boson theory to study the spin transport in the biquadratic Heisenberg chains in a square lattice with a distribution of non-magnetic impurities on the lattice. We verify the influence of the site dilution in the Ac and Dc spin conductivities of this model in the Bose-Einstein condensation regime in which the bosons t are condensed. Our results show that the decreasing of the gap Δ with -β suffers a change for different concentrations x of non-magnetic impurities, however the point (in the -β axis) where the gap cancels does not change with x. Therefore, the size of the region ω, where the spin conductivity goes to zero decreases with the increase of x until the point where x=0.5, where the size of this region tends to zero.
Renormalization-group studies of antiferromagnetic chains. I. Nearest-neighbor interactions
The real-space renormalization-group method introduced by workers at the Stanford Linear Accelerator Center (SLAC) is used to study one-dimensional antiferromagnetic chains at zero temperature. Calculations using three-site blocks (for the Heisenberg-Ising model) and two-site blocks (for the isotropic Heisenberg model) are compared with exact results. In connection with the two-site calculation a duality transformation is introduced under which the isotropic Heisenberg model is self-dual. Such duality transformations can be defined for models other than those considered here, and may be useful in various block-spin calculations
Euler-Heisenberg-Weiss action for QCD +QED
Ozaki, Sho; Arai, Takashi; Hattori, Koichi; Itakura, Kazunori
2015-07-01
We derive an analytic expression for one-loop effective action of QCD +QED at zero and finite temperatures by using the Schwinger proper time method. The result is a nonlinear effective action not only for electromagnetic and chromo-electromagnetic fields but also for the Polyakov loop, and thus reproduces the Euler-Heisenberg action in QED, QCD, and QED +QCD , and also the Weiss potential for the Polyakov loop at finite temperature. As applications of this "Euler-Heisenberg-Weiss" action in QCD +QED , we investigate quark pair productions induced by QCD +QED fields at zero temperature and the Polyakov loop in the presence of strong electromagnetic fields. Quark one-loop contribution to the effective potential of the Polyakov loop explicitly breaks the center symmetry, and is found to be enhanced by the magnetic field, which is consistent with the inverse magnetic catalysis observed in lattice QCD simulation.
Euler-Heisenberg-Weiss action for QCD+QED
Ozaki, Sho; Hattori, Koichi; Itakura, Kazunori
2015-01-01
We derive an analytic expression for one-loop effective action of QCD+QED at zero and finite temperatures by using the Schwinger's proper time method. The result is a nonlinear effective action not only for electromagnetic and chromo-electromagnetic fields but also the Polyakov loop, and thus reproduces the Euler-Heisenberg action in QED, QCD, and QED+QCD, and also the Weiss potential for the Polyakov loop at finite temperature. As applications of this "Euler-Heisenberg-Weiss" action in QCD+QED, we investigate quark pair productions induced by QCD+QED fields at zero temperature and the Polyakov loop in the presence of strong electromagnetic fields. Quark one-loop contribution to the effective potential of the Polyakov loop explicitly breaks the center symmetry, and is found to be enhanced by the magnetic field, which is consistent with the inverse magnetic catalysis observed in lattice QCD simulation.
Heisenberg picture approach to the stability of quantum Markov systems
Pan, Yu, E-mail: yu.pan@anu.edu.au, E-mail: zibo.miao@anu.edu.au; Miao, Zibo, E-mail: yu.pan@anu.edu.au, E-mail: zibo.miao@anu.edu.au [Research School of Engineering, Australian National University, Canberra, ACT 0200 (Australia); Amini, Hadis, E-mail: nhamini@stanford.edu [Edward L. Ginzton Laboratory, Stanford University, Stanford, California 94305 (United States); Gough, John, E-mail: jug@aber.ac.uk [Institute of Mathematics and Physics, Aberystwyth University, SY23 3BZ Wales (United Kingdom); Ugrinovskii, Valery, E-mail: v.ugrinovskii@gmail.com [School of Engineering and Information Technology, University of New South Wales at ADFA, Canberra, ACT 2600 (Australia); James, Matthew R., E-mail: matthew.james@anu.edu.au [ARC Centre for Quantum Computation and Communication Technology, Research School of Engineering, Australian National University, Canberra, ACT 0200 (Australia)
2014-06-15
Quantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such systems. Lyapunov-type conditions in the Heisenberg picture are derived in order to stabilize the evolution of system operators as well as the underlying dynamics of the quantum states. In particular, using the quantum Markov semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. Furthermore, this paper proves the quantum invariance principle, which extends the LaSalle invariance principle to quantum systems in the Heisenberg picture. These results are formulated in terms of algebraic constraints suitable for engineering quantum systems that are used in coherent feedback networks.
Space Group Symmetry Fractionalization in a Chiral Kagome Heisenberg Antiferromagnet.
Zaletel, Michael P; Zhu, Zhenyue; Lu, Yuan-Ming; Vishwanath, Ashvin; White, Steven R
2016-05-13
The anyonic excitations of a spin liquid can feature fractional quantum numbers under space group symmetries. Detecting these fractional quantum numbers, which are analogs of the fractional charge of Laughlin quasiparticles, may prove easier than the direct observation of anyonic braiding and statistics. Motivated by the recent numerical discovery of spin-liquid phases in the kagome Heisenberg antiferromagnet, we theoretically predict the pattern of space group symmetry fractionalization in the kagome lattice SO(3)-symmetric chiral spin liquid. We provide a method to detect these fractional quantum numbers in finite-size numerics which is simple to implement in the density matrix renormalization group. Applying these developments to the chiral spin liquid phase of a kagome Heisenberg model, we find perfect agreement between our theoretical prediction and numerical observations. PMID:27232041
The role of phase space geometry in Heisenberg's uncertainty relation
Aiming towards a geometric description of quantum theory, we study the coherent states-induced metric on the phase space, which provides a geometric formulation of the Heisenberg uncertainty relations (both the position-momentum and the time-energy ones). The metric also distinguishes the original uncertainty relations of Heisenberg from the ones that are obtained from non-commutativity of operators. Conversely, the uncertainty relations can be written in terms of this metric only, hence they can be formulated for any physical system, including ones with non-trivial phase space. Moreover, the metric is a key ingredient of the probability structure of continuous-time histories on phase space. This fact allows a simple new proof the impossibility of the physical manifestation of the quantum Zeno and anti-Zeno paradoxes. Finally, we construct the coherent states for a spinless relativistic particle, as a non-trivial example by which we demonstrate our results
Influence of the Heisenberg Principle on the Ideal Bose Gas
Zheng, Hua; Bonasera, Aldo
2013-01-01
The ideal Bose gas has two major shortcomings: at zero temperature, all the particles 'condense' at zero energy or momentum, thus violating the Heisenberg principle; the second is that the pressure below the critical point is independent of density resulting in zero incompressibility (or infinite isothermal compressibility) which is unphysical. We propose a modification of the ideal Bose gas to take into account the Heisenberg principle. This modification results in a finite (in)compressibility at all temperatures and densities. The main properties of the ideal Bose gas are preserved, i.e. the relation between the critical temperature and density, but the specific heat has a maximum at the critical temperature instead of a discontinuity. Of course interactions are crucial for both cases in order to describe actual physical systems.
Laguerre calculus and Paneitz operator on the Heisenberg group
CHANG; Der-Chen
2009-01-01
Laguerre calculus is a powerful tool for harmonic analysis on the Heisenberg group.Many sub-elliptic partial differential operators can be inverted by Laguerre calculus.In this article,we use Laguerre calculus to find explicit kernels of the fundamental solution for the Paneitz operator and its heat equation.The Paneitz operator which plays an important role in CR geometry can be written as follows:Here{Zj}n j=1 is an orthonormal basis for the subbundle T(1,0)of the complex tangent bundle TC(Hn) and T is the"missing direction".The operator Lα is the sub-Laplacian on the Heisenberg group which is sub-elliptic ifαdoes not belong to an exceptional setΛα.We also construct projection operators and relative fundamental solution for the operator Lα whileα∈Λα.
Wavelet transform and Radon transform on the Quaternion Heisenberg group
He, JIanxun
2011-01-01
Let $\\mathscr Q$ be the quaternion Heisenberg group, and let $\\mathbf P$ be the affine automorphism group of $\\mathscr Q$. We develop the theory of continuous wavelet transform on the quaternion Heisenberg group via the unitary representations of $\\mathbf P$ on $L^2(\\mathscr Q)$. A class of radial wavelets is constructed. The inverse wavelet transform is simplified by using radial wavelets. Then we investigate the Radon transform on $\\mathscr Q$. A Semyanistri-Lizorkin space is introduced, on which the Radon transform is a bijection. We deal with the Radon transform on $\\mathscr Q$ both by the Euclidean Fourier transform and the group Fourier transform. These two treatments are essentially equivalent. We also give an inversion formula by using wavelets, which does not require the smoothness of functions if the wavelet is smooth.
Approaching the Heisenberg Limit without Single-Particle Detection.
Davis, Emily; Bentsen, Gregory; Schleier-Smith, Monika
2016-02-01
We propose an approach to quantum phase estimation that can attain precision near the Heisenberg limit without requiring single-particle-resolved state detection. We show that the "one-axis twisting" interaction, well known for generating spin squeezing in atomic ensembles, can also amplify the output signal of an entanglement-enhanced interferometer to facilitate readout. Applying this interaction-based readout to oversqueezed, non-Gaussian states yields a Heisenberg scaling in phase sensitivity, which persists in the presence of detection noise as large as the quantum projection noise of an unentangled ensemble. Even in dissipative implementations-e.g., employing light-mediated interactions in an optical cavity or Rydberg dressing-the method significantly relaxes the detection resolution required for spectroscopy beyond the standard quantum limit. PMID:26894711
Rogue-wave interaction for the Heisenberg ferromagnetism system
Heisenberg-type models for spin–spin interactions have been used to explain magnetic ordering in ferromagnetic materials. In this paper, a generalized, inhomogeneous, nonlinear Schrödinger equation for the Heisenberg ferromagnetic spin system is investigated. By virtue of the generalized Darboux transformation, higher-order rogue-wave solutions are derived. Wave propagation and interaction are analyzed: (1) bright-rogue waves are found; (2) perturbation parametes and inhomogeneities in the medium of the system affect the direction and existing time of the first-order rogue-wave propagation; (3) perturbation parameters and inhomogeneities in the medium of the system affect the shapes, distances, patterns, and existing times of the second- and third-order rogue-wave interactions; (4) the direction of each second-order rogue wave remains unvaried after the interaction. (paper)
Heisenberg picture approach to the stability of quantum Markov systems
Quantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such systems. Lyapunov-type conditions in the Heisenberg picture are derived in order to stabilize the evolution of system operators as well as the underlying dynamics of the quantum states. In particular, using the quantum Markov semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. Furthermore, this paper proves the quantum invariance principle, which extends the LaSalle invariance principle to quantum systems in the Heisenberg picture. These results are formulated in terms of algebraic constraints suitable for engineering quantum systems that are used in coherent feedback networks
Investigation of non-Hermitian Hamiltonians in the Heisenberg picture
Miao, Yan-Gang; Xu, Zhen-Ming
2016-05-01
The Heisenberg picture for non-Hermitian but η-pseudo-Hermitian Hamiltonian systems is suggested. If a non-Hermitian but η-pseudo-Hermitian Hamiltonian leads to real second order equations of motion, though their first order Heisenberg equations of motion are complex, we can construct a Hermitian counterpart that gives the same second order equations of motion. In terms of a similarity transformation we verify the iso-spectral property of the Hermitian and non-Hermitian Hamiltonians and obtain the related eigenfunctions. This feature can be used to determine real eigenvalues for such non-Hermitian Hamiltonian systems. As an application, two new non-Hermitian Hamiltonians are constructed and investigated, where one is non-Hermitian and non-PT-symmetric and the other is non-Hermitian but PT-symmetric. Moreover, the complementarity and compatibility between our treatment and the PT symmetry are discussed.
Inspiration of Heisenberg Uncertainty Principle to College Education
梁讯
2008-01-01
No matter how accurately one tried to measure the classical quantities of position and momentum, there would always be an uncertainty in the measurement.The Heisenberg Principle of Uncertainty is one of the most significant changes in our comprehension of the universe, it inspired people once again to think the unthinkable, and challenge the very foundations of subjects in both research and educational fields.
Magnetic properties of nanoscale compass-Heisenberg planar clusters
Trousselet, F.; Oles, A. M.; Horsch, P.
2012-01-01
We study a model of spins 1/2 on a square lattice, generalizing the quantum compass model via the addition of perturbing Heisenberg interactions between nearest neighbors, and investigate its phase diagram and magnetic excitations. This model has motivations both from the field of strongly correlated systems with orbital degeneracy and from that of solid-state based devices proposed for quantum computing. We find that the high degeneracy of ground states of the compass model is fragile and ch...
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.
New relativistic generalization of the Heisenberg commutation relations
A relativistic generalization of the Heisenberg commutation relations is suggested which is different from the conventional ones used for the intrinsic coordinates and momenta in the relativistic oscillator model and the relativistic string. This new quantum relativistic oscillator (QRC) model is determined by the requirement that it gives a unified description of relativistic vibrations and rotations and contracts in the non-relativistic limit 1/c → 0 into the usual non-relativistic harmonic oscillator. 10 refs
Graph model of the Heisenberg-Weyl algebra
Blasiak, P.; Horzela, A.; Duchamp, G. H. E.; Penson, K. A.; Solomon, A. I.
2007-01-01
We consider an algebraic formulation of Quantum Theory and develop a combinatorial model of the Heisenberg-Weyl algebra structure. It is shown that by lifting this structure to the richer algebra of graph operator calculus, we gain a simple interpretation involving, for example, the natural composition of graphs. This provides a deeper insight into the algebraic structure of Quantum Theory and sheds light on the intrinsic combinatorial underpinning of its abstract formalism.
Graph model of the Heisenberg-Weyl algebra
We consider an algebraic formulation of Quantum Theory and develop a combinatorial model of the Heisenberg-Weyl algebra structure. It is shown that by lifting this structure to the richer algebra of graph operator calculus, we gain a simple interpretation involving, for example, the natural composition of graphs. This provides a deeper insight into the algebraic structure of Quantum Theory and sheds light on the intrinsic combinatorial underpinning of its abstract formalism.
The Stabilized Poincare-Heisenberg algebra: a Clifford algebra viewpoint
Gresnigt, N. G.; Renaud, P. F.; Butler, P. H.
2006-01-01
The stabilized Poincare-Heisenberg algebra (SPHA) is the Lie algebra of quantum relativistic kinematics generated by fifteen generators. It is obtained from imposing stability conditions after attempting to combine the Lie algebras of quantum mechanics and relativity which by themselves are stable, however not when combined. In this paper we show how the sixteen dimensional Clifford algebra CL(1,3) can be used to generate the SPHA. The Clifford algebra path to the SPHA avoids the traditional ...
Random field distributed Heisenberg model on a thin film geometry
The effects of the bimodal random field distribution on the thermal and magnetic properties of the Heisenberg thin film have been investigated by making use of a two spin cluster with the decoupling approximation. Particular attention has been devoted to the obtaining of phase diagrams and magnetization behaviors. The physical behaviors of special as well as tricritical points are discussed for a wide range of selected Hamiltonian parameters. For example, it is found that when the strength of a magnetic field increases, the locations of the special point (which is the ratio of the surface exchange interaction and the exchange interaction of the inner layers that makes the critical temperature of the film independent of the thickness) in the related plane decrease. Moreover, tricritical behavior has been obtained for higher values of the magnetic field, and influences of the varying Hamiltonian parameters on its behavior have been elucidated in detail in order to have a better understanding of the mechanism underlying the considered system. - Highlights: • Effect of bimodal random field distribution within the Heisenberg model is investigated. • Phase diagrams of the random field Heisenberg model in a thin film geometry are obtained. • Effect of the random field on the magnetic properties is obtained. • Variation of the special point with random field is determined. • Variation of the tricritical point with random field is determined
The spin-Peierls chain revisited
Hager, Georg; Weisse, Alexander; Wellein, Gerhard; Jeckelmann, Eric; Fehske, Holger
2006-01-01
We extend previous analytical studies of the ground-state phase diagram of a one-dimensional Heisenberg spin chain coupled to optical phonons, which for increasing spin-lattice coupling undergoes a quantum phase transition from a gap-less to a gaped phase with finite lattice dimerisation. We check the analytical results against established four-block and new two-block density matrix renormalisation group (DMRG) calculations. Different finite-size scaling behaviour of the spin excitation gaps ...
Jing Wen LUAN; Fu Liu ZHU
2005-01-01
In this paper, we make the asymptotic estimates of the heat kernel for the quaternionic Heisenberg group in various cases. We also use these results to deduce the asymptotic estimates of certain harmonic functions on the quaternionic Heisenberg group. Moreover a Martin compactification of the quaternionic Heisenberg group is constructed, and we prove that the Martin boundary of this group is homeomorphic to the unit ball in the quaternionic field.
Quantum theory of spin waves in finite chiral spin chains
Roldán-Molina, A.; Santander, M. J.; Núñez, A.S.; Fernández Rossier, Joaquín
2013-01-01
We calculate the effect of spin waves on the properties of finite-size spin chains with a chiral spin ground state observed on biatomic Fe chains deposited on iridium(001). The system is described with a Heisenberg model supplemented with a Dzyaloshinskii-Moriya coupling and a uniaxial single ion anisotropy that presents a chiral spin ground state. Spin waves are studied using the Holstein-Primakoff boson representation of spin operators. Both the renormalized ground state and the elementary ...
YAO Xiao-yan; LI Peng-lei; DONG Shuai; LIU Jun-ming
2007-01-01
A three-dimensional Ising-like model doped with anti-ferromagnetic (AFM) bonds is proposed to investigate the magnetic properties of a doped triangular spin-chain system by using a Monte-Carlo simulation. The simulated results indicate that a steplike magnetization behavior is very sensitive to the concentration of AFM bonds. A low concentration of AFM bonds can suppress the stepwise behavior considerably, in accordance with doping experiments on Ca3Co206. The analysis of spin snapshots demonstrates that the AFM bond doping not only breaks the ferromagnetic ordered linear spin chains along the hexagonal c-axis but also has a great influence upon the spin configuration in the ab-plane.
Hierarchy of Local Minimum Solutions of Heisenberg's Uncertainty Principle
We derive a new hierarchy of local minimum Heisenberg-uncertainty states by introducing a superposition of ''small waves'' onto some initial state. Our objective is to increase the resolution in one observable, with the least decrease in the resolution in the conjugate observable. This leads to a constrained minimization which in a well-defined sense yields the best possible way of achieving this goal. The results are relevant to many topics (e.g., quantum optics and control, Bose-Einstein condensation, path integration, etc.)
Some Properties of Quasiconvex Functions on the Heisenberg Group
Ming-bao Sun; Xiao-ping Yang
2005-01-01
For the Heisenberg group, we introduce the concept of h-quasiconvex functions. We prove that the notions of h-quasiconvex functions and h-convex set are equivalent and that h-quasiconvex functions are locally bounded from above, and furthermore derive that h-convex functions are locally bounded, therefore it is locally Lipschitz continuous by using recent results by Danielli-Garofalo-Nhieu. Finally we give estimates of the L∞norm of the first derivatives of h-quasiconvex functions.
Bootstrap equations and correlation functions for the Heisenberg XYZ antiferromagnet
Quano, Yas-Hiro
2002-01-01
Presented are two kinds of integral solutions to the quantum Knizhnik-Zamolodchikov equations for the 2n-point correlation functions of the Heisenberg XYZ antiferromagnet. Our first integral solution can be obtained from those for the cyclic SOS model by using the vertex-face correspondence. By the construction, the sum with respect to the local height variables k_0, k_1, >..., k_{2n} of the cyclic SOS model remains other than n-fold integral in the first solution. In order to perform those s...
Wavelet Coefficients Energy Redistribution and Heisenberg Principle of Uncertainty
Vošvrda, Miloslav; Schurrer, J.
Plzeň : University of West Bohemia, Plzeň, 2015, s. 894-899. ISBN 978-80-261-0539-8. [Mathematical Methods in Economics 2015 /33./. Cheb (CZ), 09.09.2015-11.09.2015] R&D Projects: GA ČR(CZ) GBP402/12/G097 Institutional support: RVO:67985556 Keywords : Heisenberg Principle of Uncertainty * signal energy * Wavelet Transformation * signal entropy Subject RIV: AH - Economics http://library.utia.cas.cz/separaty/2015/E/vosvrda-0449775.pdf
Yang-Lee Circle Theorem for an Antiferromagnetic Heisenberg Ladder
王先智
2001-01-01
The Yang-Lee zeros of an antiferromagnetic Heisenberg ladder model are determined. It is found that if J4≤0 Yang-Lee zeros are located on the unit circle and on the negative real axis in the complex activity plane. In particular, if J4≤0 and 2J2≥J4, Yang-Lee zeros are located on the unit circle and the Yang-Lee circle theorem is valid. If J4 ＞ 0, Yang-Lee zeros are located on some complicated curves.
Critical magnetic scattering from the Heisenberg ferromagnet EuS
The paramagnetic scattering from the insulating, isotropic ferromagnet EuS is investigated at T/sub c/ along the [111] direction by means of inelastic neutron scattering. The energy width of the quasielastic scattering is proportional to q/sup z/ with z = 2.54 +- 0.10, in good agreement with the predictions of dynamical scaling theory (z = 2.5). z is, however, significantly larger than the value deduced from measurements along the [100] direction (z = 2.2). Near the zone boundary the magnetic scattering exhibits shoulders the shapes of which deviate from theoretical predictions based on the Heisenberg model. 19 refs., 3 figs
Deformed Heisenberg algebra: origin of q-calculus
Swamy, P. Narayana
2003-01-01
The intimate connection between q-deformed Heisenberg uncertainty relation and the Jackson derivative based on q-basic numbers has been noted in the literature. The purpose of this work is to establish this connection in a clear and self-consistent formulation and to show explicitly how the Jackson derivative arises naturally. We utilize a holomorphic representation to arrive at the correct algebra to describe q-deformed bosons. We investigate the algebra of q-fermions and point out how diffe...
On the uniqueness of the unitary representations of the non commutative Heisenberg-Weyl algebra
Gouba, Laure; Scholtz, Frederik G.
2009-01-01
In this paper we discuss the uniqueness of the unitary representations of the non commutative Heisenberg-Weyl algebra. We show that, apart from a critical line for the non commutative position and momentum parameters, the Stone-von Neumann theorem still holds, which implies uniqueness of the unitary representation of the Heisenberg-Weyl algebra.
K-theory, cyclic cohomology and pairings for quantum Heisenberg manifolds
Gabriel, Olivier
2013-01-01
The C*-algebras called quantum Heisenberg manifolds (QHMs) were introduced by Rieffel in 1989 as strict deformation quantizations of Heisenberg manifolds. It was later shown that they are also examples of generalized crossed products. In this article, we compute the pairings of K-theory and cyclic...... Chern characters of the K-theory....
An index formula for the extended Heisenberg algebra of Epstein, Melrose and Mendoza
van Erp, Erik
2010-01-01
The extended Heisenberg algebra for a contact manifold contains, as subalgebras, both the Heisenberg algebra as well as the classical pseudodifferential operators. We derive here a formula for the index of Fredholm operators in this extended calculus. This formula incorporates in a single expression the Atiyah-Singer formula for elliptic operators, as well as Boutet de Monvel's Toeplitz index formula.
We juxtapose two approaches to the representations of the super-Heisenberg group. Physical one, sometimes called concrete approach, based on the super-wave functions depending on the anti-commuting variables, yielding the harmonic superanalysis and recently developed strict theory of unitary representations of the nilpotent super Lie groups covering the unitary representations of the super-Heisenberg group