Spin Chain Model Research Articles

Disordered Heisenberg XYZ magnetic chains with exponential correlations: Localization and quantum state transfer

Our study investigates the Quantum State Transfer Protocol within a one-dimensional quantum Heisenberg spin chain model that features exponentially correlated disorder in the spin coupling distribution. We conducted extensive numerical simulations to explore how varying degrees of correlation impact the transfer of quantum states through this model of a quantum channel. Our results demonstrate that the extent of correlation significantly influences quantum communication along the channel. Specifically, we observed that in the strongly correlated regime, quantum communication remains largely unaffected even in large systems. These findings are interpreted in the context of the localization properties inherent to the disordered channel.

Smooth crossover between weak and strong thermalization using rigorous bounds on equilibration of isolated systems

It is usually expected and observed that non-integrable isolated quantum systems thermalize. However, for some non-integrable spin chain models, in a numerical study, initial states with oscillations that persisted for some time were found and the phenomenon was named weak thermalization. Later, it was argued that such oscillations will eventually decay suggesting that weak thermalization was about time scales and not the size of the fluctuations. Nevertheless, the analyses of the size of the fluctuations were more qualitative. Here, using exact diagonalization we analyze how the size of the typical fluctuation, after long enough time for equilibration to happen, scales with the system size. For that, we use rigorous mathematical upper bounds on the equilibration of isolated quantum systems. We show that weak thermalization can be understood to be due to the small effective dimension of the initial state. Furthermore, we show that the fluctuations decay exponentially with the system size for both weak and strong thermalization indicating no sharp transitions between these two regimes.

Asymptotics of block Toeplitz determinants with piecewise continuous symbols

AbstractWe determine the asymptotics of the block Toeplitz determinants as for matrix‐valued piecewise continuous functions with a finitely many jumps under mild additional conditions. In particular, we prove that where , , and are constants that depend on the matrix symbol and are described in our main results. Our approach is based on a new localization theorem for Toeplitz determinants, a new method of computing the Fredholm index of Toeplitz operators with piecewise continuous matrix‐valued symbols, and other operator theoretic methods. As an application of our results, we consider piecewise continuous symbols that arise in the study of entanglement entropy in quantum spin chain models.

Quantum inception score

Motivated by the great success of classical generative models in machine learning, enthusiastic exploration of their quantum version has recently started. To depart on this journey, it is important to develop a relevant metric to evaluate the quality of quantum generative models; in the classical case, one such example is the (classical) inception score (cIS). In this paper, as a natural extension of cIS, we propose the quantum inception score (qIS) for quantum generators. Importantly, qIS relates the quality to the Holevo information of the quantum channel that classifies a given dataset. In this context, we show several properties of qIS. First, qIS is greater than or equal to the corresponding cIS, which is defined through projection measurements on the system output. Second, the difference between qIS and cIS arises from the presence of quantum coherence, as characterized by the resource theory of asymmetry. Third, when a set of entangled generators is prepared, there exists a classifying process leading to the further enhancement of qIS. Fourth, we harness the quantum fluctuation theorem to characterize the physical limitation of qIS. Finally, we apply qIS to assess the quality of the one-dimensional spin chain model as a quantum generative model, with the quantum convolutional neural network as a quantum classifier, for the phase classification problem in the quantum many-body physics. Published by the American Physical Society 2024

Quantum Battery in the Heisenberg Spin Chain Models with Dzyaloshinskii‐Moriya Interaction

AbstractQuantum battery (QB) is an energy storage and extraction device conforming to the principles of quantum mechanics. In this study, the characteristics of QBs are considered for the Heisenberg spin chain models in the absence and presence of Dzyaloshinskii‐Moriya (DM) interaction. The results show that the DM interaction can enhance the ergotropy and power of QBs, which shows the collective charging can outperform parallel charging regarding QB's performance. Besides, it turns out that first‐order coherence is a crucial quantum resource during charging, while quantum steering between the cells is not conducive to the energy storage of QBs. The investigations offer insight into the properties of QBs with Heisenberg spin chain models with DM interaction and facilitate us to acquire the performance in the framework of realistic quantum batteries.

A Q-Operator for Open Spin Chains II: Boundary Factorization

One of the features of Baxter’s Q-operators for many closed spin chain models is that all transfer matrices arise as products of two Q-operators with shifts in the spectral parameter. In the representation-theoretical approach to Q-operators, underlying this is a factorization formula for L-operators (solutions of the Yang–Baxter equation associated to particular infinite-dimensional representations). To extend such a formalism to open spin chains, one needs a factorization identity for solutions of the reflection equation (boundary Yang–Baxter equation) associated to these representations. In the case of quantum affine sl2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathfrak {sl}_2$$\\end{document} and diagonal K-matrices, we derive such an identity using the recently formulated theory of universal K-matrices for quantum affine algebras.

Bethe/Gauge correspondence for AN spin chains with integrable boundaries

We continue the survey initiated in [1] to explore the Bethe/Gauge correspondence between supersymmetric SO/Sp gauge theories in 2d/3d/4d and open spin chain with integrable boundaries. We collect the known Bethe ansatz equations of different types of spin chains with general boundaries that have been analyzed in the literature, and compare them with the vacua equations of the quiver gauge theories. It seems that not all the vacua equations of quiver gauge theory with BCD-type gauge groups can be realized as some known Bethe ansatz equations of integrable spin chain models.

Dephasing effects on nonclassical correlations in two-qubit Heisenberg spin chain model with anisotropic spin–orbit interactions

Dephasing effects on nonclassical correlations in two-qubit Heisenberg spin chain model with anisotropic spin–orbit interactions

Rényi entanglement asymmetry in ( 1+1 )-dimensional conformal field theories

In this paper, we consider the Rényi entanglement asymmetry of excited states in the (1+1) dimensional free compact boson conformal field theory (CFT) at equilibrium. We obtain a universal CFT expression written by correlation functions for the charged moments via the replica trick. We provide detailed analytic computations of the second Rényi entanglement asymmetry in the free compact boson CFT for excited states Ψ=Vβ+V−β and Φ=Vβ+J with Vβ and J=i∂ϕ being the vertex operator and current operator, respectively. We make numerical tests of the universal CFT computations using the XX spin chain model. Taking the non-Hermite fake reduced density matrices into consideration, we propose an effective way to test them numerically, which can be applied to other excited states. The CFT predictions are in perfect agreement with the exact numerical calculations. Published by the American Physical Society 2024

Petz recovery from subsystems in conformal field theory

We probe the multipartite entanglement structure of the vacuum state of a CFT in 1+1 dimensions, using recovery operations that attempt to reconstruct the density matrix in some region from its reduced density matrices on smaller subregions. We use an explicit recovery channel known as the twirled Petz map, and study distance measures such as the fidelity, relative entropy, and trace distance between the original state and the recovered state. One setup we study in detail involves three contiguous intervals A, B and C on a spatial slice, where we can view these quantities as measuring correlations between A and C that are not mediated by the region B that lies between them. We show that each of the distance measures is both UV finite and independent of the operator content of the CFT, and hence depends only on the central charge and the cross-ratio of the intervals. We evaluate these universal quantities numerically using lattice simulations in critical spin chain models, and derive their analytic forms in the limit where A and C are close using the OPE expansion. In the case where A and C are far apart, we find a surprising non-commutativity of the replica trick with the OPE limit. For all values of the cross-ratio, the fidelity is strictly better than a general information-theoretic lower bound in terms of the conditional mutual information. We also compare the mutual information between various subsystems in the original and recovered states, which leads to a more qualitative understanding of the differences between them. Further, we introduce generalizations of the recovery operation to more than three adjacent intervals, for which the fidelity is again universal with respect to the operator content.

Multifractal dimensions for orthogonal-to-unitary crossover ensemble.

Multifractal analysis is a powerful approach for characterizing ergodic or localized nature of eigenstates in complex quantum systems. In this context, the eigenvectors of random matrices belonging to invariant ensembles naturally serve as models for ergodic states. However, it has been found that the finite-size versions of multifractal dimensions for these eigenvectors converge to unity logarithmically slowly with increasing system size N. In fact, this strong finite-size effect is capable of distinguishing the ergodicity behavior of orthogonal and unitary invariant classes. Motivated by this observation, in this work, we provide semi-analytical expressions for the ensemble-averaged multifractal dimensions associated with eigenvectors in the orthogonal-to-unitary crossover ensemble. Additionally, we explore shifted and scaled variants of multifractal dimensions, which, in contrast to the multifractal dimensions themselves, yield distinct values in the orthogonal and unitary limits as N→∞ and, therefore, may serve as a convenient measure for studying the crossover. We substantiate our results using Monte Carlo simulations of the underlying crossover random matrix model. We then apply our results to analyze the multifractal dimensions in a quantum kicked rotor, a Sinai billiard system, and a correlated spin-chain model in a random field. The orthogonal-to-unitary crossover in these systems is realized by tuning relevant system parameters, and we find that in the crossover regime, the observed finite-dimension multifractal dimensions can be captured very well with our results.

Robustness and Eventual Slow Decay of Bound States of Interacting Microwave Photons in the Google Quantum AI Experiment

Integrable models are characterized by the existence of stable excitations that can propagate indefinitely without decaying. This includes multimagnon bound states in the celebrated XXZ spin-chain model and its integrable Floquet counterpart. A recent Google Quantum AI experiment [A. Morvan , Nature , 240 (2022)] realizing the Floquet model has demonstrated the persistence of such collective excitations even when the integrability is broken: this observation is at odds with the expectation of ergodic dynamics in generic nonintegrable systems. Here, we study the spectrum of the model realized in the experiment using exact diagonalization and physical arguments. We find that isolated bands corresponding to the descendants of the exact bound states of the integrable model are clearly observable in the spectrum for a large range of system sizes. However, our numerical analysis of the localization properties of the eigenstates suggests that the bound states become unstable in the thermodynamic limit. A perturbative estimate of the decay rate agrees with the prediction of an eventual instability for large system sizes. Published by the American Physical Society 2024

New soliton solutions and dynamical analysis of (2+1)-dimensional Heisenberg ferromagnetic spin-chain model arising in quantum information

In this paper, the soliton solutions of (2+1)-dimensional Heisenberg ferromagnetic spin-chain model arising in quantum information are obtained using G′/(bG′+G′+a)-Expansion Method. The solutions of the model are plotted in 2d and 3D graphs to show the dynamics of the solutions with effect of the model parameters. Bifurcations and chaotic behavior are analyzed, providing insights into the system’s dynamics. Our results offer a valuable mathematical tool for studying nonlinear wave phenomena, including the discovery of new wave shapes, bifurcations, and chaotic dynamics. The novel application of the G′/(bG′+G+a)-Expansion Method uncovers previously unreported solutions, while the study of bifurcations and chaos enhances our understanding of the model’s applicability.

Long-ranged spectral correlations in eigenstate phases

We study non-local measures of spectral correlations and their utility in characterizing and distinguishing between the distinct eigenstate phases of quantum chaotic and many-body localized systems. We focus on two related quantities, the spectral form factor and the density of all spectral gaps, and show that they furnish unique signatures that can be used to sharply identify the two phases. We demonstrate this by numerically studying three one-dimensional quantum spin chain models with (i) quenched disorder, (ii) periodic drive (Floquet), and (iii) quasiperiodic detuning. We also clarify in what ways the signatures are universal and in what ways they are not. More generally, this thorough analysis is expected to play a useful role in classifying phases of disorder systems.

Stability analysis and soliton solutions of truncated M-fractional Heisenberg ferromagnetic spin chain model via two analytical methods

Stability analysis and soliton solutions of truncated M-fractional Heisenberg ferromagnetic spin chain model via two analytical methods

Mapping between space-like curve flows and soliton equations in Minkowski space

In this study, we demonstrate that when three distinct moving space-like curves with the time-like binormal vectors satisfy the generalizations of the Heisenberg spin chain model, these models are equivalent to the third-order system of the AKNS hierarchy and the complex KdV-type equations.

Generalized phase-space techniques to explore quantum phase transitions in critical quantum spin systems

We apply the generalized Wigner function formalism to detect and characterize a range of quantum phase transitions in several cyclic, finite-length, spin-12 one-dimensional spin-chain models, viz., the Ising and anisotropic XY models in a transverse field, and the XXZ anisotropic Heisenberg model. We make use of the finite system size to provide an exhaustive exploration of each system’s single-site, bipartite and multi-partite correlation functions. In turn, we are able to demonstrate the utility of phase-space techniques in detecting and characterizing first-order, second-order and infinite-order quantum phase transitions, while also enabling an in-depth analysis of the correlations present within critical systems. We also highlight the method’s ability to capture other features of spin systems such as ground-state factorization and critical system scaling. Finally, we demonstrate the generalized Wigner function’s utility for state verification by determining the state of each system and their constituent sub-systems at points of interest across the quantum phase transitions, enabling interesting features of critical systems to be readily analyzed.

Lieb-Schultz-Mattis, Luttinger, and 't Hooft - anomaly matching in lattice systems

We analyze lattice Hamiltonian systems whose global symmetries have ’t Hooft anomalies. As is common in the study of anomalies, they are probed by coupling the system to classical background gauge fields. For flat fields (vanishing field strength), the nonzero spatial components of the gauge fields can be thought of as twisted boundary conditions, or equivalently, as topological defects. The symmetries of the twisted Hilbert space and their representations capture the anomalies. We demonstrate this approach with a number of examples. In some of them, the anomalous symmetries are internal symmetries of the lattice system, but they do not act on-site. (We clarify the notion of “on-site action.”) In other cases, the anomalous symmetries involve lattice translations. Using this approach we frame many known and new results in a unified fashion. In this work, we limit ourselves to 1+1d systems with a spatial lattice. In particular, we present a lattice system that flows to the c=1c=1 compact boson system with any radius (no BKT transition) with the full internal symmetry of the continuum theory, with its anomalies and its T-duality. As another application, we analyze various spin chain models and phrase their Lieb-Shultz-Mattis theorem as an ’t Hooft anomaly matching condition. We also show in what sense filling constraints like Luttinger theorem can and cannot be viewed as reflecting an anomaly. As a by-product, our understanding allows us to use information from the continuum theory to derive some exact results in lattice model of interest, such as the lattice momenta of the low-energy states.

Control of Quantum‐Memory Induced by Generated Thermal XYZ‐Heisenberg Entanglement: y‐Component DM Interaction

AbstractThis study explores the thermal quantum‐memory‐assisted entropic uncertainty relation (QM‐EUR) and entanglement in a general two‐qubit XYZ‐Heisenberg spin chain model in the presence of the Dzyaloshinskii–Moriya (DM) interaction. The characterization of y‐component DM and spin–spin interactions are particularly focused. It is found that the DM and spin–spin interaction strengths highly regulate the flow behavior and the initial final levels of QM‐EUR and entanglement. In comparison, the spin–spin interaction strength in the z‐direction remains useful in both ferromagnetic and anti‐ferromagnetic regimes for entropic uncertainty suppression and entanglement generation. Additionally, the negative and the positive directed DM values can usefully turn classical states into resourceful quantum states. The dynamics of thermal QM‐EUR and entanglement‐of‐formation have symmetric behaviors only with respect to y‐component DM and z‐component spin–spin interaction. Finally, different critical points of temperature, component DM as well as spin–spin interaction are encountered, which should be opted to preserve quantum correlations and degrade uncertainty.

New and more solitary wave patterns of the Heisenberg ferromagnetic spin chain model in fiber optics

The primary focus of this paper is the determination of novel soliton solutions for the [Formula: see text]-dimensional Heisenberg ferromagnetic spin chain (HFSC) problem. The suggested model may be thought of as a special case of the nonlinear Schrödinger equation. Exact solutions to the proposed equation have been found using efficient analytical approaches such as the singular manifold method and the [Formula: see text]-expansion method. These proposed methods are significant mathematical tools to obtain the exact traveling wave solutions of nonlinear complex partial differential equations (PDEs). After decomposing the governing problem into its real and imaginary components, we analyze both the real and imaginary components separately. Soliton solutions are obtained using computational tools like Maple. Trigonometric function solutions, rational solutions and hyperbolic function solutions are found for Heisenberg ferromagnetic model by the application of the proposed techniques. Furthermore, the physical properties of the solutions, such as hyperbolic functions, are important. The hyperbolic tangent is used in the computation of magnetic moment and velocity in special relativity. As a result, we hypothesize that the obtained results have physically comparable meanings to those stated by these collocations. By selecting suitable values of arbitrary parameters, it has been observed graphically that the amplitude of obtained solutions can be changed. Graphical representations of few of the reported solutions are presented in both two and three dimensions by choosing appropriate values of parameters. The suggested approaches are very efficient and reliable for finding exact solutions of wide range of nonlinear PDEs in a complex medium. The advantage of these techniques is evident since they are not limited in their ability to locate such wave patterns. Back substitution in the original equation using Maple 18 validated all solutions found, and the physical significance of these results has been underlined. The constraint conditions for the existence of constructed solutions are also provided in this paper.