XXZ Heisenberg Chain Research Articles

Local quantum Fisher information and quantum correlation in the mixed-spin Heisenberg XXZ chain

Local quantum Fisher information and quantum correlation in the mixed-spin Heisenberg XXZ chain

Exploring large-scale entanglement in quantum simulation.

Entanglement is a distinguishing feature of quantum many-body systems, and uncovering the entanglement structure for large particle numbers in quantum simulation experiments is a fundamental challenge in quantum information science1. Here we perform experimental investigations of entanglement on the basis of the entanglement Hamiltonian (EH)2 as an effective description of the reduceddensity operator for large subsystems. We prepare ground and excited states of a one-dimensional XXZ Heisenberg chain on a 51-ion programmable quantum simulator3 and perform sample-efficient 'learning' of the EH for subsystems of up to 20 lattice sites4. Our experiments provide compelling evidence for a local structure of the EH. To our knowledge, this observation marks the first instance of confirming the fundamental predictions of quantum field theory by Bisognano and Wichmann5,6, adapted to lattice models that represent correlated quantum matter. The reduced state takes the form of a Gibbs ensemble, with a spatially varying temperature profile as a signature of entanglement2. Our results also show the transition from area- to volume-law scaling7 of von Neumann entanglement entropies from ground to excited states. As we venture towards achieving quantum advantage, we anticipate that our findings and methods have wide-ranging applicability to revealing and understanding entanglement in many-body problems with local interactions including higher spatial dimensions.

Magnon boundary states tailored by longitudinal spin–spin interactions and topology

Since longitudinal spin–spin interaction is ubiquitous in magnetic materials, it is very interesting to explore the interplay between topology and longitudinal spin–spin interaction. Here, we examine the role of longitudinal spin–spin interaction on topological magnon excitations. Remarkably, even for single-magnon excitations, we discover topological edge states and defect edge states of magnon excitations in a dimerized Heisenberg XXZ chain and their topological properties can be distinguished via adiabatic quantum transport. We uncover topological phase transitions induced by longitudinal spin–spin interactions whose boundary is analytically obtained via the transfer matrix method. For multi-magnon excitations, even-magnon bound states are found to be always topologically trivial, but odd-magnon bound states may be topologically nontrivial due to the interplay between the transverse dimerization and the longitudinal spin–spin interaction. For two-dimensional spin systems, the longitudinal spin–spin interaction contributes to the coexistence of defect corner states, second-order topological corner states and first-order topological edge states. We propose an experimental scheme to realize and measure the magnon boundary states in superconducting qubits. Our work opens an avenue for exploring topological magnon excitations and has potential applications in topological magnon devices.

Finite temperature properties of an integrable zigzag ladder chain

We consider the interaction-round-a-face version of the six-vertex model for arbitrary anisotropy parameter, which allow us to derive an integrable one-dimensional quantum Hamiltonian with three-spin interactions. We apply the quantum transfer matrix approach for the face model version of the six-vertex model. The integrable quantum Hamiltonian shares some thermodynamical properties with the Heisenberg XXZ chain, but has different ordering and critical exponents. Two gapped phases are the dimerized antiferromagnetic order and the usual antiferromagnetic (Néel) order for positive nearest neighbor Ising coupling. In between these, there is an extended critical region, which is a quantum spin-liquid with broken parity symmetry inducing an oscillatory behavior at the long distance <σ1zσℓ+1z> correlation. At finite temperatures, the numerical solution of the non-linear integral equations allows for the determination of the correlation length as well as for the momentum of the oscillation.

Optimal local work extraction from bipartite quantum systems in the presence of Hamiltonian couplings

We investigate the problem of finding the local analogue of the ergotropy, that is the maximum work that can be extracted from a system if we can only apply local unitary transformation acting on a given subsystem. In particular, we provide a closed formula for the local ergotropy in the special case in which the local system has only two levels, and give analytic lower bounds and semidefinite programming upper bounds for the general case. As non-trivial examples of application, we compute the local ergotropy for a atom in an electromagnetic cavity with Jaynes-Cummings coupling, and the local ergotropy for a spin site in an XXZ Heisenberg chain, showing that the amount of work that can be extracted with an unitary operation on the coupled system can be greater than the work obtainable by quenching off the coupling with the environment before the unitary transformation.

Exact solutions of few-magnon problems in the spin- S periodic XXZ chain

We solve few-magnon problems for a finite-size spin-$S$ periodic Heisenberg XXZ chain with single-ion anisotropy through constructing sets of exact Bloch states achieving block diagonalization of the system. Concretely, the two-magnon (three-magnon) problem is converted to a single-particle one on a one-dimensional (two-dimensional) effective lattice whose size depends linearly (quadratically) on the total number of sites. For parameters lying within certain ranges, various types of multimagnon bound states are manifested and shown to correspond to edge states on the effective lattices. In the absence of the single-ion anisotropy, we reveal the condition under which exact zero-energy states emerge. As applications of the formalism, we calculate the transverse dynamic structure factor for a higher-spin chain near saturation magnetization and find signatures of the multimagnon bound states. We also calculate the real-time three-magnon dynamics from certain localized states, which are relevant to cold-atom quantum simulations, by simulating single-particle quantum walks on the effective lattices. This provides a physically transparent interpretation of the observed dynamics in terms of propagation of bound state excitations. Our method can be directly applied to more general spin or itinerant particle systems possessing translational symmetry.

Integrable hard-rod deformation of the Heisenberg spin chains.

We present integrable models of interacting spin-1/2 chains which can be interpreted as hard-rod deformations of the XXZ Heisenberg chains. The models support multiple particle types: Dynamical hard rods of length ℓ and particles with lengths ℓ^{'}<ℓ that are immobile except for the interaction with the hard rods. We encounter a remarkable phenomenon in these interacting models: Exact spectral degeneracies across different deformations and volumes. The algebraic integrability of these systems is also treated using a recently developed formalism for medium-range integrable spin chains. We present the detailed Bethe Ansatz solution for the case ℓ=2.

Long-lived nonthermal states in pumped one-dimensional systems of hard-core bosons

We study a unitary time evolution of a symmetry-broken state in a form of a charge density wave in a finite system of interacting hard-core bosons, which can be mapped onto the XXZ Heisenberg chain. Moreover, we introduce a spatially-homogenous and time-dependent vector potential that mimics a short laser pulse. We establish the range of amplitudes of the vector potential for which the onset of charge density wave order can be controlled. We propose a protocol that reveals non-thermal long-lived states, which are characterized by a non-zero charge density wave order translated by one lattice site with respect to its initial formation. The life times of these states are large in comparison to all typical times given by the parameters of the system. They increase with the number of lattice sites, but are significantly suppressed by the integrablility breaking perturbations. In view of these findings, we speculate that the long-lived non-thermal states exist in the thermodynamic limit.

Collision rate ansatz for quantum integrable systems

For quantum integrable systems the currents averaged with respect to a generalized Gibbs ensemble are revisited. An exact formula is known, which we call ``collision rate ansatz". While there is considerable work to confirm this ansatz in various models, our approach uses the symmetry of the current-charge susceptibility matrix, which holds in great generality. Besides some technical assumptions, the main input is the availability of a self-conserved current, i.e. some current which is itself conserved. The collision rate ansatz is then derived. The argument is carried out in detail for the Lieb-Liniger model and the Heisenberg XXZ chain. It is also explained how from the existence of a boost operator a self-conserved current can be deduced.

Time evolution of entanglement in a four-qubit Heisenberg chain

The phenomenon of quantum entanglement has a very important role in quantum mechanics. Particularly, the quantum spin chain provides a platform for theoretical and experimental investigation of many-body entanglement. In this paper, we investigate time evolution of entanglement in a four-qubit anisotropic Heisenberg XXZ chain with nearest neighboring (NN), the next nearest neighboring (NNN), and the Dzialoshinskii-Moriya (DM) interactions. Calculations of the entanglement evolution of the Werner state carried out in terms of concurrence for selected ranges of control parameters such as DM interaction, frustration, etc. The results show that for the Werner state, DM interaction and the frustration parameters play important roles. Furthermore, results show that the time evolution of the Werner state entanglement may be useful to capture the quantum phase transitions in quantum magnetic systems.

Topological Basis Realization Associated with Spin-1 Non-Hermitian XXZ Model

We investigate the spin-1 topological basis realization of a non-Hermitian Heisenberg XXZ chain model. For the non-Hermitian case, the Hamiltonian and the topological ground states of the system are constructed by Birman-Murakami-Wenzl algebra. The results show that all the spin singlet states belong to the topological ground states. The topological subspace and the spin singlet subspace are equivalent. The topological basis can reduce Birman-Murakami-Wenzl algebra generators, and the reduced matrices satisfy reduced Birman-Murakami-Wenzl algebra relations.

Geometric phase and topological phase diagram of the one-dimensional XXZ Heisenberg spin chain in a longitudinal field

In this paper, we determine the geometric phase for the one-dimensional XXZ Heisenberg chain with spin-1/2, the exchange couple J and the spin anisotropy parameter Δ in a longitudinal field (LF) with the reduced field strength h. Using the Jordan-Wigner transformation and the mean-field theory based on the Wick’s theorem, a semi-analytical theory has been developed in terms of order parameters which satisfy the self-consistent equations. The values of the order parameters are numerically computed using the matrix-product-state (MPS) method. The validity of the mean-filed theory could be checked through the comparison between the self-consistent solutions and the numerical results. Finally, we draw the topological phase diagrams in the case J<0 and the case J>0.

Energy current manipulation and reversal of rectification in graded XXZ spin chains

This work is devoted to the investigation of nontrivial transport properties in many-body quantum systems. Precisely, we study transport in the steady state of spin-1/2 Heisenberg XXZ chains, driven out of equilibrium by two magnetic baths at their end points. We take graded versions of the model, i.e. asymmetric chains in which some structure gradually changes in space. We investigate how we can manipulate and control the energy and spin currents of such chains by tuning external and/or inner parameters. In particular, we describe the occurrence of energy current rectification and its reversal due to the application of external magnetic fields. We show that, after carefully chosen inner parameters for the system, by turning on an external magnetic field we can find spin and energy currents propagating in different directions. More interestingly, we may find cases in which rectifications of energy and spin currents occur in opposite directions, i.e. if the energy current is larger when flowing from left to right side, then the spin current is larger if it flows from right to left side. We still describe situations with inversion of the energy current direction as we increase the system asymmetry. We stress that our work aims the development of theoretical knowledge as well as the stimulation of future experimental applications.

How order melts after quantum quenches

Injecting a sufficiently large energy density into an isolated many-particle system prepared in a state with long-range order will lead to the melting of the order over time. Detailed information about this process can be derived from the quantum mechanical probability distribution of the order parameter. We study this process for the paradigmatic case of the spin-1/2 Heisenberg XXZ chain. We determine the full quantum mechanical distribution function of the staggered subsystem magnetization as a function of time after a quantum quench from the classical N\'eel state. This provides a detailed picture of how the N\'eel order melts and reveals the existence of an interesting regime at intermediate times that is characterized by a very broad probability distribution.

Magnetic phase transitions of insulating spin-orbit coupled Bose atoms in one-dimensional optical lattices

We consider the insulating spin-orbit coupled Bose atoms confined within one-dimensional optical lattices and explore their ground-state magnetic phase transitions. Under strong interactions, the charge degrees of atoms are frozen and the system can be described by an anisotropic XXZ Heisenberg chain with Dzyaloshinskii-Moriya interaction and transverse field. We apply the matrix product state method to obtain low-energy states and analyze the lowest energy gaps and the ground-state magnetization and correlations. We find when the transverse field is absent, the ground state is a gapped ferromagnetic phase with long-range correlation in the z direction if the interspin s-wave interacting strength is stronger than that of the intraspin one, otherwise it is a gapless Luttinger liquid (LL) phase with algebraic decaying correlation. When the transverse field is turned on, the gapless LL phase is broken, there emerges a long-range correlated phase with ferromagnetic, antiferromagnetic or spiral order, which depends on the DM interaction strength. We believe our study provides a complete understanding of the interplay between SOC and quantum magnetism of spinor atoms in optical lattices.

Switching pure states of the dissipative Heisenberg XXZ chain by local magnetic fields

The effects of a local magnetic field on nonequilibrium stationary states (NESS) of the open quantum $XXZ$ spin chain are investigated with a Lindblad master equation approach in the limit of strong dissipation. The local magnetic field is applied to a single bulk spin of the chain while the ends are kept at fixed polarizations by dissipation. We show that suitable changes of the local magnetic field permit to invert the spin current by switching pure NESS with opposite chiralities, while preserving the state purity and achieving optimal transport.

Finite-time quantum quenches in the XXZ Heisenberg chain

We study the time evolution of the two-point correlation functions in the XXZ Heisenberg chain after a finite-time quantum quench in the anisotropy. We compare results from numerical simulations to ones obtained in the Luttinger model and find good agreement. We analyse the spreading of the correlations and the associated light-cone features. We observe a delay in the appearance of the light cone as compared to the sudden-quench setup, and link this delay to the properties of the quench protocol.

Typical growth behavior of the out-of-time-ordered commutator in many-body localized systems

We investigate the typicality of the growth behavior of the out-of-time-ordered commutator (OTOC) in the many-body localized (MBL) quantum spin chains across random disorder realizations. In the MBL phase of the Heisenberg XXZ chain, we find that the estimate of the OTOC fluctuates significantly with the disorder realizations at the intermediate times of the main growth. Despite the consequent failure of the disorder average in the MBL phase, we argue that the characteristic behavior of the OTOC growth can still be identified by going through individual disorder realizations. We find that a power-law-type growth behavior appears typically after a disorder-dependent relaxation period, which is very close to the $t^2$ form derived in the effective Hamiltonian of a fully MBL system. The characteristic growth behavior observed at an individual disorder realization is robust in our tests with various state preparations and also verified in another MBL system of the random-transverse-field quantum Ising chain in a uniform longitudinal field.

Specific heat and thermal entanglement in an open quantum system

In this paper, the density matrix is obtained using the non-Markovian master equation method for a system consisting of two-qubit modeling with the Heisenberg XXZ chain, which involves the Dzyaloshinskii–Moriya interaction and is exposed to the bosonic baths. Also, using the proposed formula for calculating the specific heat through the density matrix of the open quantum system, the specific heat is calculated. The quantum entanglement behavior with time and coupling constant is investigated. It is observed that the specific heat at low temperatures becomes negative when the system is exposed to the environment. The time behavior of quantum entanglement for this model showed that the entanglement decreases to zero with increasing time.

From Kondo effect to weak-link regime in quantum spin- 12 spin chains

We analyze the crossover from Kondo to weak-link regime by means of a model of tunable bond impurities in the middle of a spin-1/2 XXZ Heisenberg chain. We study the Kondo screening cloud and estimate the Kondo length by combining perturbative renormalization group approach with the exact numerical calculation of the integrated real-space spin-spin correlation functions. We show that, when the spin impurity is symmetrically coupled to the two parts of the chain with realistic values of the Kondo coupling strengths and spin-parity symmetry is preserved, the Kondo length takes values within the reach of nowadays experimental technology in ultracold-atom setups. In the case of non-symmetric Kondo couplings and/or spin parity broken by a nonzero magnetic field applied to the impurity, we discuss how Kondo screening redistributes among the chain as a function of the asymmetry in the couplings and map out the shrinking of the Kondo length when the magnetic field induces a crossover from Kondo impurity to weak-link physics.