Antiferromagnetic XXZ Model Research Articles

Quantum correlation, entanglement in the kagome lattice non-Hermitian quantum systems

Quantum correlation in the antiferromagnetic XXZ model on kagome lattice and non-Hermitian tight binding model on kagome lattice are investigated. For the Hermitian XXZ model on kagome lattice, the calculations are performed for different extensions of the model with single-ion anisotropy and out-of-plane Dzyaloshinskii–Moriya interaction (DMI). We get the von Neumann entropy as a function of the DMI interaction, anisotropy and single-ion anisotropy with aim to verify the effect of these corrections that occurs in real magnetic systems on quantum correlation. Moreover, the effect of DMI interaction, anisotropy and single-ion anisotropy is investigated on concurrence and entanglement negativity as well. For the non-Hermitian tight binding model on kagome lattice, we analyzed quantum correlation using the entanglement negativity as entanglement measure which is more adequate in this case.

Continuous similarity transformation for critical phenomena: Easy-axis antiferromagnetic XXZ model

We apply continuous similarity transformations (CSTs) to the easy-axis antiferromagnetic XXZ-model on the square lattice. The CST flow equations are truncated in momentum space by the scaling dimension $d$ so that all contributions with $d\le 2$ are taken into account. The resulting quartic magnon-conserving effective Hamiltonian is analyzed in the zero-, one-, and two-magnon sector. In this way, a quantitative description of the ground-state energy, the one-magnon dispersion and its gap as well as of two-magnon bound states is gained for anisotropies ranging from the gapped Ising model to the gapless Heisenberg model. We discuss the critical properties of the gap closing as well as the evolution of the one-magnon roton mininum. The excitation energies of two-magnon bound states are calculated and their decay into the two-magnon continuum is determined via the inverse participation ratio.

Entanglement Negativity and Concurrence in Some Low-Dimensional Spin Systems.

The influence of magnon bands on entanglement in the antiferromagnetic XXZ model on a triangular lattice, which models the bilayer structure consisting of an antiferromagnetic insulator and normal metal, is investigated. This effect was studied in ferromagnetic as well as antiferromagnetic triangular lattices. Quantum entanglement measures given by the entanglement negativity have been studied, where a magnon current is induced in the antiferromagnet due to interfacial exchange coupling between localized spins in the antiferromagnet and itinerant electrons in a normal metal. Moreover, quantum correlations in other frustrated models, namely the metal-insulation antiferromagnetic bilayer model and the Heisenberg model with biquadratic and bicubic interactions, are analyzed.

Magnon valley thermal Hall effect in triangular-lattice antiferromagnets

We study the magnetic excitations of the antiferromagnetic XXZ model on two-dimensional triangular lattice. We find there is a magnon valley thermal Hall effect. As far as we know, this effect has been studied on only the ferromagnetic honeycomb lattice. We reveal that the valley thermal Hall conductivity also conforms to the universal behavior of thermal Hall conductivity proposed by Yang et al. [Phys. Rev. Lett. 124, 186602 (2020)]. We derive a low-energy effective theory near the valleys and find that although the low-energy effective dynamic matrix is non-Hermitian, the Berry curvatures are mainly determined by its Hermitian part. We show that our results are general to some extent in the Y phase of the triangular lattice. By an explicit calculation with experimental parameters, we demonstrate that ${\mathrm{Rb}}_{4}\mathrm{Mn}{({\mathrm{MoO}}_{4})}_{3}$ is a suitable material to realize the magnon valley thermal Hall effect.

Effects of magnetic anisotropy on spin and thermal transport in classical antiferromagnets on the square lattice

Transport properties of the classical antiferromagnetic XXZ model on the square lattice have been theoretically investigated, putting emphasis on how the occurrence of a phase transition is reflected in spin and thermal transports. As is well known, the anisotropy of the exchange interaction $\mathrm{\ensuremath{\Delta}}\ensuremath{\equiv}{J}_{z}/{J}_{x}$ plays a role to control the universality class of the transition of the model, i.e., either a second-order transition at ${T}_{N}$ into a magnetically ordered state or the Kosterlitz-Thouless (KT) transition at ${T}_{\text{KT}}$, which respectively occur for the Ising-type ($\mathrm{\ensuremath{\Delta}}>1$) and XY-type ($\mathrm{\ensuremath{\Delta}}<1$) anisotropies, while for the isotropic Heisenberg case of $\mathrm{\ensuremath{\Delta}}=1$, a phase transition does not occur at any finite temperature. It is found by means of the hybrid Monte Carlo and spin-dynamics simulations that the spin current probes the difference in the ordering properties, while the thermal current does not. For the XY-type anisotropy, the longitudinal spin-current conductivity ${\ensuremath{\sigma}}_{xx}^{s}$ ($={\ensuremath{\sigma}}_{yy}^{s}$) exhibits a divergence at ${T}_{\text{KT}}$ of the exponential form ${\ensuremath{\sigma}}_{xx}^{s}\ensuremath{\propto}exp\left[B/\sqrt{T/{T}_{\text{KT}}\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}\right]$ with $B=O(1)$, while for the Ising-type anisotropy, the temperature dependence of ${\ensuremath{\sigma}}_{xx}^{s}$ is almost monotonic without showing a clear anomaly at ${T}_{N}$ and such a monotonic behavior is also the case in the Heisenberg-type spin system. The significant enhancement of ${\ensuremath{\sigma}}_{xx}^{s}$ at ${T}_{\text{KT}}$ is found to be due to the exponential rapid growth of the spin-current relaxation time toward ${T}_{\text{KT}}$, which can be understood as a manifestation of the topological nature of a vortex whose lifetime is expected to get longer toward ${T}_{\text{KT}}$. Possible experimental platforms for the spin-transport phenomena associated with the KT topological transition are discussed.

Quantum entanglement and critical exponents in one-dimensional spin-1 bond-alternating XXZ chains

The characterization of the quantum phase transition in a lowdimensional system has attracted a considerable amount of attention in quantum manybody systems. As one of the fundamental models in quantum magnetism, spin-1 models have richer phase diagrams and show more complex physical phenomena. In the spin-1 antiferromagnetic XXZ model, the Haldane phase and the Nel phase are the gapped topologic phases which cannot be characterized by the local order parameters. To characterize the nature in such phases, one has to calculate the non-local long range order parameters. Normally, the non-local order parameter in the topological phase is obtained from the extrapolation of finite-sized system in numerical study. However, it is difficult to extract the critical exponents with such an extrapolated non-local order parameter due to the numerical accuracy. In a recently developed tensor network representation, i.e., the infinite matrix product state (iMPS) algorithm, it was shown that the non-local order can be directly calculated from a very large lattice distance in an infinite-sized system rather than an extrapolated order parameter in a finite-sized system. Therefore, it is worthwhile using this convenient technique to study the non-local orders in the topological phases and characterize the quantum criticalities in the topological quantum phase transitions. In this paper, by utilizing the infinite matrix product state algorithm based on the tensor network representation and infinite time evolving block decimation method, the quantum entanglement, fidelity, and critical exponents of the topological phase transition are investigated in the one-dimensional infinite spin-1 bond-alternating XXZ Heisenberg model. It is found that there is always a local dimerization order existing in the whole parameter range when the bond-alternative strength parameter changes from 0 to 1. Also, due to the effect of the bond-alternating, there appears a quantum phase transition from the long-rang ordering topological Nel phase to the local ordering dimerization phase. The von Neumann entropy, fidelity per lattice site, and order parameters all give the same phase transition point at c = 0.638. To identify the type of quantum phase transition, the central charge c 0.5 is extracted from the ground state von Neumann entropy and the finite correlation length, which indicates that the phase transition belongs to the two-dimensional Ising universality class. Furthermore, it is found that the Nel order and the susceptibility of Nel order have power-law relations to |-c|. From the numerical fitting of the Nel order and its susceptibility, we obtain the characteristic critical exponents ' = 0.236 and ' = 0.838. It indicates that such critical exponents from our method characterize the nature of the quantum phase transition. Our critical exponents from the iMPS method can provide guidance for studying the properties of the phase transition in quantum spin systems.

Geometric entanglement and quantum phase transitions in two-dimensional quantum lattice models

Geometric entanglement(GE), as a measure of multipartite entanglement, has been investigated as a universal tool to detect phase transitions in quantum many-body lattice models. We outline a systematic method to compute GE for two-dimensional (2D) quantum many-body lattice models based on the translational invariant structure of infinite projected entangled pair state (iPEPS) representations. By employing this method, the $q$-state quantum Potts model on the square lattice with $q \in \{2, 3 ,4, 5\}$ is investigated as a prototypical example. Further, we have explored three 2D Heisenberg models, such as the spin-$\frac{1}{2}$ XXX and antiferromagnetic anisotropic XYX models in an external magnetic field, and the spin-1 antiferromagnetic XXZ model. We find that continuous GE does not guarantee a continuous phase transition across a phase transition point. We observe and thus classify three different types of continuous GE across a phase transition point: (i) GE is continuous with maximum value at the transition point and the phase transition is continuous, (ii) GE is continuous with maximum value at the transition point but the phase transition is discontinuous, and (iii) GE is continuous with non-maximum value at the transition point and the phase transition is continuous. For the models under consideration we find that the second and the third types are related to a point of dual symmetry and a fully polarized phase, respectively.

Phase diagram of the antiferromagnetic XXZ model on the triangular lattice

We determine the quantum phase diagram of the antiferromagnetic spin-1/2 XXZ model on the triangular lattice as a function of magnetic field and anisotropic coupling $J_z$. Using the density matrix renormalization group (DMRG) algorithm in two dimensions we establish the locations of the phase boundaries between a plateau phase with 1/3 N\'eel order and two distinct coplanar phases. The two coplanar phases are characterized by a simultaneous breaking of both translational and U(1) symmetries, which is reminiscent of supersolidity. A translationally invariant umbrella phase is entered via a first order phase transition at relatively small values of $J_z$ compared to the corresponding case of ferromagnetic hopping and the classical model. The phase transition lines meet at two tricritical points on the tip of the lobe of the plateau state, so that the two coplanar states are completely disconnected. Interestingly, the phase transition between the plateau state and the upper coplanar state changes from second order to first order for large values of $J_z > 2.5J$.

Universal corrections to the entanglement entropy in gapped quantum spin chains: A numerical study

We carry out a numerical study of the bi-partite entanglement entropy in the gapped regime of two paradigmatic quantum spin chain models: the Ising chain in an external magnetic field and the anti-ferromagnetic XXZ model. The universal scaling limit of these models is described by the massive Ising field theory and the SU(2)-Thirring (sine-Gordon) model, respectively. We may therefore exploit quantum field theoretical results to predict the behaviour of the entropy. We numerically confirm that, in the scaling limit, corrections to the saturation of the entropy at large region size are proportional to the Bessel function K0(2mr) where m is a mass scale (the inverse correlation length) and r the length of the region under consideration. The proportionality constant is simply related to the number of particle types in the universal spectrum. This was originally predicted in publications involving two of the current authors for two-dimensional quantum field theories. Away from the universal region our numerics suggest an entropic behaviour following quite closely the quantum field theory prediction, except for extra dependencies on the correlation length.

Critical scales in anisotropic spin systems from functional renormalization

We apply a recently developed functional renormalization group (fRG) scheme for quantum spin systems to the spin-1/2 antiferromagnetic XXZ model on a two-dimensional square lattice. Based on an auxiliary fermion representation we derive flow equations which allow a resummation of the perturbation series in the spin-spin interactions. Spin susceptibilities are calculated for different values of the anisotropy parameter. The phase transition between planar and axial ordering at the isotropic point is reproduced correctly. The results for the critical scales from the fRG as quantitative measures for the ordering temperatures are in good agreement with the exact solution in the Ising limit. On the easy-plane side, the deviations from critical temperatures obtained with quantum Monte Carlo are larger but still acceptable. However, at the isotropic point the Mermin-Wagner theorem is violated such that a precise description of the behavior in the vicinity of the phase transition is not possible. We discuss possible reasons for these discrepanies.

Coupled-cluster calculations for the ground and excited states of the spin-half XXZ model

The coupled-cluster method is applied to the spin-1/2 antiferromagnetic XXZ model on a square lattice by employing an approximation which contains two-body long-range correlations and high-order four-body local correlations. Improvement is found for the ground-state energy, the sublattice magnetization and the critical anisotropy when comparing with the approximation including the two-body correlations alone. We also obtain the full excitation spectrum which is in good agreement with the quantum Monte Carlo results and the high-order spin-wave theory.

Numerical study of spin-1/2 XXZ model on square lattice from tensor productstates

By means of the recently proposed algorithm based on the tensor product states,the magnetization process of the spin-1/2 antiferromagnetic XXZ model on asquare lattice is investigated. In the large spin-anisotropy limit, clear evidence of afirst-order spin–flip transition is observed as an external magnetic field is increased.Our findings of the critical field and the discrete jumps in various local orderparameters are in good agreement with the quantum Monte Carlo data in theliterature. Our results imply that this algorithm can be an accurate and efficientnumerical approach in studying first-order quantum phase transitions in twodimensions.

A non-Hermitian analysis of strongly correlated quantum systems

We study a non-Hermitian generalization of strongly correlated quantum systems in which the transfer energy of electrons is asymmetric. It is known that a non-Hermitian critical point is equal to the inverse localization length of a Hermitian non-interacting random electron system. We here conjecture that we can obtain in the same way the correlation length of a Hermitian interacting non-random system. We confirm the conjecture using exact solutions and numerical finite-size data of the Hubbard model and the antiferromagnetic XXZ model in one dimension.

On the Absence of Non-Periodic Ground States for the Antiferromagnetic XXZ Model

We prove that the antiferromagnetic XXZ model with Ising-like anisotropy on a one-dimensional lattice does not have non-periodic ground states.

Tensor Product State Formulation for the Spin 1/2 Antiferromagnetic XXZ Model on the Checkerboard Lattice

Vertical density matrix algorithm (VDMA), a tensor product state formulation of the ``higher-dimensional'' density matrix renormalization group, is applied to the spin 1/2 antiferromagnetic XXZ model on the checkerboard lattice. The VDMA was, in the preceding study, applied to the transverse field Ising model on the square lattice and the three-dimensional classical Ising model. In the present paper, its implementation procedure is modified in order to apply the VDMA to the XXZ model. Numerical accuracy of the VDMA is investigated for the XXZ model on the square lattice, which shows that the method gives reliable results for the ground state energy. In the frustrated region, VDMA results are compared with a simple calculation based on a magnetically disordered state. It is found that the weakly frustrated region is in the N\'{e}el ordered phase, while in the strongly frustrated region the realized phase cannot be identified clearly by the obtained results.

Spin wave theory for antiferromagneticXXZspin model on a triangle lattice in the presence of an external magnetic field

Spin wave theory is applied to a quantum antiferromagnetic XXZ model on a triangle lattice in the presence of an in-plane magnetic field. The effect of the field is found to enhance the quantum fluctuation and to reduce the sublattice magnetization at the intermediate field strength in the anisotropic case. The possible implication to the field driven quantum phase transition from a spin solid to a spin liquid is discussed.

Disordered Ground‐State Properties of the Double‐Layer Antiferromagnetic Quantum XXZ Model

The double-layer antiferromagnetic quantum XXZ model is studied by the bond-operator mean-field theory. The transverse and longitudinal modes in excited spectra, and the phase diagram for disorder-order phase transition about Δ and J/J⊥, which are the relative strength of spin anisotropy and the ratio of the intralayer coupling to the interlayer coupling, respectively, are obtained. It is found that the critical ratio of (J/J⊥) c is 0.174 for XY model (Δ = 0), and is 0.430 for isotropic model (Δ = 1). In the disordered phase and on the critical points, the excitation spectra are analyzed. The spin gap from the condensed spin singlets to the first excited states, the ground state energy and the spin wave velocities in the disordered state are calculated as functions of parameters Δ and J/J⊥.

Exact solution of the one-dimensional anisotropic t - J model: ground-state properties and the excitation spectrum

The one-dimensional anisotropic t - J model was exactly solved using the Bethe ansatz. We first discuss the effect of anisotropy on the ground-state properties. We find a continuous phase transition induced by a magnetic field. The low-lying (spin and charge) excitation spectrum is obtained for various fillings. According to the anisotropy, the model has massive or massless modes for spin excitations. At half-filling, the model reduces to the spin- antiferromagnetic XXZ-model. We calculate the correct excitation continuum whose lowest mode is lower than that obtained by des Cloizeaux and Gaudin. Charge excitations are massless for any value of the anisotropy.

Quantum correction to the BKT transition for 2D easy-plane antiferromagnets

We consider the quantum antiferromagnet with easy-plane exchange anisotropy, namely, the antiferromagnetic XXZ model, on the square lattice. Its classical counterpart, compared to the planar model shows a reduction of the critical temperature TBKT of the Berezinskii–Kosterlitz–Thouless phase transition, that is a consequence of the thermal out-of-plane fluctuations. For the quantum system we use the pure-quantum self-consistent harmonic approximation to calculate how much the effective exchange interaction is weakened as an effect of the pure-quantum part of the fluctuations. One can then predict the further reduction of TBKT with respect to the corresponding classical system. The theory works well in a wide range of values of the easy-plane anisotropy. In the extreme case of the spin-1/2 model, the result is compatible with the estimate of TBKT obtained by previous quantum Monte Carlo simulations. When the anisotropy is weak the theory leads to an unphysical ‘‘isotropization’’ due to the use of the Villain spin-boson transformation.

The antiferromagnetic spin- 1/2 -XXZ model on rings with an odd number of sites

The ground-state energies of the antiferromagnetic XXZ model at a given spin are determined on chains with an odd number N of sites. Analytical and numerical solutions of the Bethe ansatz equations are compared for the N-even and N-odd case. The scaling properties of the ground-state energies enable the determination of the zero-temperature susceptibility. For the isotropic case, we analyse the logarithmic terms in the low-field limit.