One-dimensional XXZ Model Research Articles

Crossover behaviors of entanglement dynamics at the critical point in XXZ spin chain

In this paper, we investigate the crossover behaviors of entanglement and return probability at the critical point in one-dimensional XXZ model by quantum renormalization group method. Two types of quench protocols (A) adding the interaction term in z spin direction suddenly and (B) rotating all the even spins by π about the z spin direction suddenly are considered to drive the dynamics of the system, respectively. The dynamical behaviors are closely related to the initial state under two types of quench protocols, especially at N→∞. For the left of critical point, return probabilities eventually approach one under both types of quench protocols. For the right of critical point, return probability oscillates between the maximum value and zero for quench A and tends to one for quench B, respectively. In addition, we discuss the evolution period of entanglement (return probability), find that it is positively and negatively correlated with N in the spin-fluid and Néel phases, respectively. By further analyzing the behaviors of entanglement, return probability and evolution period under both types of quench protocols near the critical point, we observe that they exist the same scaling behaviors, in which the exponents are identical to entanglement exponent of the stationary system, which is related to the results of renormalization group.

Dimensional reduction in quantum spin- 12 system on a 17 -depleted triangular lattice

We study the magnetism of a quantum spin-1/2 antiferromagnet on a maple-leaf lattice which is obtained by regularly depleting 1/7 of the sites of a triangular lattice. Although the interactions are set to be spatially uniform, the ground state shows a stripe Neel order and the temperature dependence of magnetic susceptibility follows that of the one-dimensional XXZ model with a finite spin gap. We examine the nature of frustration by mapping the low energy degenerate manifold of states to the fully packed loop-string model on a dual cluster-depleted honeycomb lattice, finding that the order-by-disorder due to quantum fluctuation characteristic of highly frustrated magnets is responsible for the emergent stripes. The excited magnons split into two spinons and propagate in the one-dimensional direction along the stripe which is reminiscent of the XXZ or Ising model in one dimension. Unlike most of the previously studied dimensional reduction effects, our case is purely spontaneous as the interactions of the Hamiltonian retains a spatially isotropic two-dimensional structure.

Speck of chaos

It has been shown that, despite being local, a perturbation applied to a single site of the one-dimensional XXZ model is enough to bring this interacting integrable spin-1/2 system to the chaotic regime. Here, we show that this is not unique to this model, but happens also to the Ising model in a transverse field and to the spin-1 Lai-Sutherland chain. The larger the system is, the smaller the amplitude of the local perturbation for the onset of chaos. We focus on two indicators of chaos, the correlation hole, which is a dynamical tool, and the distribution of off-diagonal elements of local observables, which is used in the eigenstate thermalization hypothesis. Both methods avoid spectrum unfolding and can detect chaos even when the eigenvalues are not separated by symmetry sectors.

Variational reduced density matrix method in the doubly-occupied configuration interaction space using four-particle N-representability conditions: Application to the XXZ model of quantum magnetism.

This work deals with the variational determination of the two-particle reduced density matrix (2-RDM) and the energy corresponding to the ground state of N-particle systems within the doubly occupied configuration interaction (DOCI) space. Here, we impose for the first time up to four-particle N-representability constraint conditions in the variational determination of the 2-RDM matrix elements using the standard semidefinite programming algorithms. The energies and 2-RDMs obtained from this treatment and the corresponding computational costs are compared with those arisen from previously reported less restrictive variational methods [D. R. Alcoba et al., J. Chem. Phys. 149, 194105 (2018)] as well as with the exact DOCI values. We apply the different approximations to the one-dimensional XXZ model of quantum magnetism, which has a rich phase diagram with one critical phase and constitutes a stringent test for the method. The numerical results show the usefulness of our treatment to achieve a high degree of accuracy.

Universal scrambling in gapless quantum spin chains

Information scrambling, characterized by the out-of-time-ordered correlator (OTOC), has attracted much attention, as it sheds new light on chaotic dynamics in quantum many-body systems. The scale invariance, which appears near the quantum critical region in condensed matter physics, is considered to be important for the fast decay of the OTOC. In this paper, we focus on the one-dimensional spin-1/2 XXZ model, which exhibits quantum criticality in a certain parameter region, and investigate the relationship between scrambling and the scale invariance. We quantify scrambling by the averaged OTOC over the Pauli operator basis, which is related to the operator space entanglement entropy (OSEE). Using the infinite time-evolving block decimation method, we numerically calculate time dependence of the OSEE in the early-time region in the thermodynamic limit. We show that the averaged OTOC decays faster in the gapless region than in the gapped region. In the gapless region, the averaged OTOC behaves in the same manner regardless of the anisotropy parameter. This result is consistent with the fact that the low-energy excitations of the gapless region belong to the same universality class as the Tomonaga-Luttinger liquid with the central charge $c=1$. Furthermore, we estimate $c$ by fitting the numerical data of the OSEE with an analytical result of the two-dimensional conformal field theory, and confirm that $c$ is close to unity. Thus, our numerical results suggest that the scale invariance leads to a universal behavior of the OTOC that is independent of the anisotropic parameter, which reflects the universality of the two-dimensional conformal field theory at low temperatures. Although the one-dimensional XXZ model is integrable, our results suggest such a universal behavior of generic nonintegrable systems, because the Tomonaga-Luttinger liquid serves as a low-energy effective theory for many nonintegrable and integrable systems. On the other hand, the OTOC in our numerical result does not exhibit the exponential decay, as our parameter regime is far from the semiclassical limit.

Quantum correlations and coherence in spin-1 Heisenberg chains

We explore quantum and classical correlations along with coherence in the ground states of spin-1 Heisenberg chains, namely the one-dimensional XXZ model and the one-dimensional bilinear biquadratic model, with the techniques of density matrix renormalization group theory. Exploiting the tools of quantum information theory, that is, by studying quantum discord, quantum mutual information and three recently introduced coherence measures in the reduced density matrix of two nearest neighbor spins in the bulk, we investigate the quantum phase transitions and special symmetry points in these models. We point out the relative strengths and weaknesses of correlation and coherence measures as figures of merit to witness the quantum phase transitions and symmetry points in the considered spin-1 Heisenberg chains. In particular, we demonstrate that as none of the studied measures can detect the infinite order Kosterlitz-Thouless transition in the XXZ model, they appear to be able to signal the existence of the same type of transition in the biliear biquadratic model. However, we argue that what is actually detected by the measures here is the SU(3) symmetry point of the model rather than the infinite order quantum phase transition. Moreover, we show in the XXZ model that examining even single site coherence can be sufficient to spotlight the second-order phase transition and the SU(2) symmetry point.

Anomalous diffusion and griffiths effects near the many-body localization transition.

We explore the high-temperature dynamics of the disordered, one-dimensional XXZ model near the many-body localization (MBL) transition, focusing on the delocalized (i.e., "metallic") phase. In the vicinity of the transition, we find that this phase has the following properties: (i)local magnetization fluctuations relax subdiffusively; (ii)the ac conductivity vanishes near zero frequency as a power law; and (iii)the distribution of resistivities becomes increasingly broad at low frequencies, approaching a power law in the zero-frequency limit. We argue that these effects can be understood in a unified way if the metallic phase near the MBL transition is a quantum Griffiths phase. We establish scaling relations between the associated exponents, assuming a scaling form of the spin-diffusion propagator. A phenomenological classical resistor-capacitor model captures all the essential features.

Effects of Bond Alternation on the Ground-State Phase Diagram of One-Dimensional XXZ Model

The ground-state properties and quantum phase transitions (QPTs) of the one-dimensional bond-alternative XXZ model are investigated by the infinite time-evolving block decimation (iTEBD) method. The bond-alternative effects on its ground-state phase diagram are discussed in detail. Once the bond alternation is taken into account, the antiferromagnetic phase (Δ > 1) will be destroyed at a given critical point and change into a disordered phase without nonlocal string order. The QPT is shown to be second-order, and the whole phase diagram is provided. For the ferromagnetic phase region (Δ < −1), the critical point rc always equals 1 (independent of Δ), and the QPT for this case is shown to be first-order. The dimerized Heisenberg model is also discussed, and two disordered phases can be distinguished by with or without nonlocal string orders. Both the bipartite entanglement and the fidelity per site, as two kinds of model-independent measures, are capable of describing all the QPTs in such a quantum model.

The excitation operator method and its application to spin dynamics in the one-dimensional XXZ model

We develop the excitation operator method, which is designed for solving the Heisenberg equation of motion by constructing excitation operators. We apply it to spin dynamics in the one-dimensional XXZ model. We find the diffusive spin transport in the gapped phase at the high temperature limit.

Wilson-Like Real-Space Renormalization Group and Low-Energy Effective Spectrum of the XXZ Chain in the Critical Regime

We present a novel real-space renormalization group(RG) for the one-dimensional XXZ model in the critical regime, reconsidering the role of the cut-off parameter in Wilson's RG for the Kondo impurity problem. We then demonstrate the RG calculation for the XXZ chain with the free boundary. Comparing the hierarchical structure of the obtained low-energy spectrum with the Bethe ansatz result, we find that the proper scaling dimension is reproduced as a fixed point of the RG transformation.

Static and dynamic properties of the XXZ chain with long-range interactions

The one-dimensional XXZ model ( s = 1 2 ) in a transverse field, with uniform long-range interactions among the transverse components of the spins, is studied. The model is exactly solved by introducing the Jordan–Wigner transformation and the integral Gaussian transformation. The complete critical behaviour and the critical surface for the quantum and classical transitions, in the space generated by the transverse field and the interaction parameters, are presented. The crossover lines for the various classical/quantum regimes are also determined exactly. It is shown that, besides the tricritical point associated with the classical transition, there are also two quantum critical points: a bicritical point where the classical second-order critical line meets the quantum critical line, and a first-order transition point at zero field. It is also shown that the phase diagram for the first-order classical/quantum transitions presents the same structure as for the second-order classical/quantum transitions. The critical classical and quantum exponents are determined, and the internal energy, the specific heat and the isothermal susceptibility, χ T zz , are presented for the different critical regimes. The two-spin static and dynamic correlation functions, 〈 S j z S l z 〉 , are also presented, and the dynamic susceptibility, χ q zz ( ω ) , is obtained in closed form. Explicit results are presented at T = 0 , and it is shown that the isothermal susceptibility, χ T zz , is different from the static one, χ q zz ( 0 ) . Finally, it is shown that, at T = 0 , the internal energy close to the first-order quantum transition satisfies the scaling form recently proposed by Continentino and Ferreira.

Entanglement and correlation in anisotropic quantum spin systems

Analytical expressions for the entanglement measures concurrence, i-concurrence and 3-tangle in terms of spin correlation functions are derived using general symmetries of the quantum spin system. These relations are exploited for the one-dimensional XXZ-model, in particular the concurrence and the critical temperature for disentanglement are calculated for finite systems with up to six qubits. A recent NMR quantum error correction experiment is analyzed within the framework of the proposed theoretical approach.

The one-dimensional XXZ model with long-range interactions

The one-dimensional XXZ model ( s= 1 2 , N sites) with uniform long-range interactions among the transverse components of the spins is considered. The Hamiltonian of the model is explicitly given by H=J∑ j=1 N s j xs j+1 x+s j ys j+1 y −(I/N) ∑ j,k=1 N s j zs k z−h∑ j=1 Ns j z, where the s x, y, z are half the Pauli spin matrices. The model is exactly solved by applying the Jordan–Wigner fermionization, followed by a Gaussian transformation. In the absence of the long-range interactions ( I=0), the model, which reduces to the isotropic XY model, is known to exhibit a second-order quantum-phase transition driven by the field at zero temperature. It is shown that in the presence of the long-range interactions ( I≠0) the nature of the transition is strongly affected. For I>0, which favours the ordering of the transverse components of the spins, the transition is changed from second to first order, due to the competition between transverse and xy couplings. On the other hand, for I>0, which induces complete frustration of the spins, a second-order transition is still present, although the system is driven out of its usual universality class, and its critical exponents assume typical mean-field values.

Phase diagram ofS=12XXZchain with next-nearest-neighbor interaction

We study the ground state properties of one-dimensional XXZ model with next-nearest neighbor coupling alpha and anisotropy Delta. We find the direct transition between the ferromagnetic phase and the spontaneously dimerized phase. This is surprising, because the ferromagnetic phase is classical, whereas the dimer phase is a purely quantum and nonmagnetic phase. We also discuss the effect of bond alternation which arises in realistic systems due to lattice distortion. Our results mean that the direct transition between the ferromagnetic and spin-Peierls phase occur.

Random-exchange disorder in the spin-1/2 XXZ chain.

The one-dimensional XXZ model is studied in the presence of disorder in the Heisenberg exchange integral. Recent predictions obtained from renormalization-group calculations are investigated numerically using a Lanczos algorithm on chains of up to 18 sites. It is found that in the presence of strong X-Y-symmetric random-exchange couplings, a ``random singlet'' phase with quasi-long-range order in the spin-spin correlations persists. As the planar anisotropy is varied, the full zero-temperature phase diagram is obtained and compared with predictions of Doty and Fisher [Phys. Rev. B 45, 2167 (1992)]. In addition, we observed a novel reentrant transition of the ordered phases when exchange disorder is included.

Linear spin-(1/2 magnetic chains: Susceptibilities, correlation functions, and applications to (C6H11NH3)CuBr3 and deuterated CuCl2

The susceptibilities, correlation functions, and correlation length of the spin-(1/2 one-dimensional XXZ model are calculated for the chains with the finite size N and free boundary conditions. The infinite-chain results are estimated by extrapolation in 1/N, and good convergence is found for most temperatures. Theoretical estimates are compared with the experimental results for the corresponding model compounds ${\mathrm{C}}_{6}$${\mathrm{H}}_{11}$${\mathrm{NH}}_{3}$${\mathrm{CuBr}}_{3}$ (CHAB-${d}_{14}$) and ${\mathrm{CuCl}}_{2}$\ensuremath{\cdot}2(${\mathrm{CH}}_{3}$${)}_{2}$SO (CDC) in the deuterated versions. The crossover region of the in-plane correlation functions is revealed and the inverse correlation length is in a semiquantitative agreement with that measured for CHAB. The single-crystal magnetic susceptibility data for CDC are reinterpreted and the quantitative agreement with the experiment is found.