arXiv subjects

Jiaozi Wang

Publications and source records attributed to Jiaozi Wang.

At least 37 records · Page 2Linked to original sources

arXiv2025

Decoherence of Histories: Chaotic Versus Integrable Systems

We study the emergence of decoherent histories in isolated systems based on exact numerical integration of the Schrödinger equation for a Heisenberg chain. We reveal that the nature of the system, which we switch from (i) chaotic to (ii) interacting integrable to (iii) non-interacting integrable, strongly impacts decoherence \new{of coarse spin observables}. From a finite size scaling law we infer a strong exponential suppression of coherences for (i), a weak exponential suppression for (ii) and no exponential suppression for (iii) on a relevant short (nonequilibrium) time scale. Moreover, for longer times we find stronger decoherence for (i) but the opposite for (ii), hinting even at a possible power-law decay for (ii) at equilibrium time scales. This behaviour is encoded in the multi-time properties of the quantum histories and it can not be explained by environmentally induced decoherence. Our results suggest that chaoticity plays a crucial role in the emergence of classicality in finite size systems.

cond-mat.stat-mech↗

arXiv2025

Observable-manifested correlations in many-body quantum chaotic systems

In this paper, we investigate the distinctions between realistic quantum chaotic systems and random models from the perspective of observable properties, particularly focusing on the eigenstate thermalization hypothesis (ETH). Through numerical simulations, we find that for realistic systems, the envelope function of off-diagonal elements of observables exhibits an exponential decay at large $ΔE$, while for randomized models, it tends to be flat. We demonstrate that the correlations of chaotic eigenstates, originating from the delicate structures of Hamiltonians, play a crucial role in the non-trivial structure of the envelope function. Furthermore, we analyze the numerical results from the perspective of the dynamical group elements in Hamiltonians. Our findings highlight the importance of correlations in physical chaotic systems and provide insights into the deviations from RMT predictions. These understandings offer valuable directions for future research.

nlin.CD↗

arXiv2025

Hydrodynamics and the eigenstate thermalization hypothesis

The eigenstate thermalization hypothesis (ETH) describes the properties of diagonal and off-diagonal matrix elements of local operators in the eigenenergy basis. In this work, we propose a relation between (i) the singular behaviour of the off-diagonal part of ETH at small energy differences, and (ii) the smooth profile of the diagonal part of ETH as a function of the energy density. We establish this connection from the decay of the autocorrelation functions of local operators, which is constrained by the presence of local conserved quantities whose evolution is described by hydrodynamics. We corroborate our predictions with numerical simulations of two non-integrable spin-1 Ising models, one diffusive and one super-diffusive, which we perform using dynamical quantum typicality up to 18 spins.

quant-ph↗

arXiv2025

Evidence for simple "arrow of time functions" in closed chaotic quantum systems

Through an explicit construction, we assign to any infinite temperature autocorrelation function $C(t)$ a set of functions $α^n(t)$. The construction of $α^n(t)$ from $C(t)$ requires the first $2n$ temporal derivatives of $C(t)$ at times $0$ and $t$. Our focus is on $α^n(t)$ that (almost) monotonously decrease, we call these ``arrows of time functions" (AOTFs). For autocorrelation functions of few body observables we numerically observe the following: An AOTF featuring a low $n$ may always be found unless the the system is in or close to a nonchaotic regime with respect to a variation of some system parameter. All $α^n(t)$ put upper bounds to the respective autocorrelation functions, i.e. $α^n(t) \geq C^2(t)$. Thus the implication of the existence of an AOTF is comparable to that of the H-Theorem, as it indicates a directed approach to equilibrium. We furthermore argue that our numerical finding may to some extent be traced back to the operator growth hypothesis. This argument is laid out in the framework of the so-called recursion method.

cond-mat.stat-mech↗

arXiv2025

Scrutinizing the Mori memory function for diffusion in periodic quantum systems

Diffusion is an ubiquitous phenomenon. It is a widespread belief that as long as the area under a current autocorrelation function converges in time, the corresponding spatiotemporal density dynamics should be diffusive. This may be viewed as a result of the combination of linear response theory with the Einstein relation. However, attempts to derive this statement from first principles are notoriously challenging. We first present a counterexample by constructing a correlation functions of some density wave, such that the area under the corresponding current autocorrelation function converges, but the dynamics do not obey a diffusion equation. Then we will introduce a method based on the recursion method and the Mori memory formalism, that may help to actually identify diffusion. For a decisive answer, one would have to know infinitely many so called Lanczos coefficients, which is unattainable in most cases. However, in the examples examined in this paper, we find that the practically computable number of Lanczos coefficients suffices for a strong guess.

cond-mat.stat-mech↗

arXiv2025

Lindblad quantum dynamics from correlation functions of classical spin chains

The Lindblad quantum master equation is one of the central approaches to the physics of open quantum systems. In particular, boundary driving enables the study of transport, where a steady state emerges in the long-time limit, which features a constant current and a characteristic density profile. While the Lindblad equation complements other approaches to transport in closed quantum systems, it has become clear that a connection between closed and open systems exists in certain cases. Here, we build on this connection for magnetization transport in the spin-1/2 XXZ chain with and without integrability-breaking perturbations. Specifically, we study the question whether the time evolution of the open quantum system can be described on the basis of classical correlation functions, as generated by the Hamiltonian equations of motion for real vectors. By comparing to exact numerical simulations of the Lindblad equation, we find a good accuracy of such a description for a range of model parameters, which is consistent with previous studies on closed systems. While this agreement is an interesting physical observation, it also suggests that classical mechanics can be used to solve the Lindblad equation for comparatively large system sizes, which lie outside the possibilities of a quantum mechanical treatment. We also point out counterexamples and limitations for the quantitative extraction of transport coefficients. Remarkably, our classical approach to large open systems allows to detect superdiffusion at the isotropic point.

cond-mat.stat-mech↗

arXiv2024

Diffusion constants from the recursion method

Understanding the transport behavior of quantum many-body systems constitutes an important physical endeavor, both experimentally and theoretically. While a reliable classification into normal and anomalous dynamics is known to be notoriously difficult for a given microscopic model, even the seemingly simpler evaluation of transport coefficients in diffusive systems continues to be a hard task in practice. This fact has motivated the development and application of various sophisticated methods and is also the main issue of this paper. We particularly take a barely used strategy, which is based Lanczos coefficients, and demonstrate that this strategy allows for the accurate calculation of diffusion coefficients for different paradigmatic examples, including magnetization transport in nonintegrable spin-1/2 chains and ladders as well as energy transport in the mixed-field Ising model in one dimension.

cond-mat.stat-mech↗

arXiv2024

Emergence of unitary symmetry of microcanonically truncated operators in chaotic quantum systems

We study statistical properties of matrix elements of observables written in the energy eigenbasis and truncated to small microcanonical windows. We present numerical evidence indicating that for all few body operators in chaotic many-body systems, truncated below certain energy scale, collective statistical properties of matrix elements exhibit emergent unitary symmetry. Namely, we show that below certain scale the spectra of the truncated operators exhibit universal behavior, matching our analytic predictions, which are numerically testable for system sizes beyond exact diagonalization. We discuss operator and system-size dependence of the energy scale of emergent unitary symmetry and put our findings in context of previous works exploring emergence of random-matrix behavior at small energy scales.

cond-mat.stat-mech↗

arXiv2023

Interplay of decoherence and relaxation in a two-level system interacting with an infinite-temperature reservoir

We study the time evolution of a single qubit in contact with a bath, within the framework of projection operator methods. Employing the so-called modified Redfield theory which also treats energy conserving interactions non-perturbatively, we are able to study the regime beyond the scope of the ordinary approach. Reduced equations of motion for the qubit are derived in a idealistic system where both the bath and system-bath interactions are modeled by Gaussian distributed random matrices. In the strong decoherence regime, a simple relation between the bath correlation function and the decoherence process induced by the energy conserving interaction is found. It implies that energy conserving interactions slow down the relaxation process, which leads to a zeno freezing if they are sufficiently strong. Furthermore, our results are also confirmed in numerical simulations.

cond-mat.stat-mech↗

arXiv2023

Estimation of equilibration time scales from nested fraction approximations

We consider an autocorrelation function of a quantum mechanical system through the lens of the so-called recursive method, by iteratively evaluating Lanczos coefficients, or solving a system of coupled differential equations in the Mori formalism. We first show that both methods are mathematically equivalent, each offering certain practical advantages. We then propose an approximation scheme to evaluate the autocorrelation function, and use it to estimate the equilibration time $τ$ for the observable in question. With only a handful of Lanczos coefficients as the input, this scheme yields an accurate order of magnitude estimate of $τ$, matching state-of-the-art numerical approaches. We develop a simple numerical scheme to estimate the precision of our method. We test our approach using several numerical examples exhibiting different relaxation dynamics. Our findings provide a new practical way to quantify the equilibration time of isolated quantum systems, a question which is both crucial and notoriously difficult.

cond-mat.stat-mech↗

arXiv2023

Classicality, Markovianity and local detailed balance from pure state dynamics

When describing the effective dynamics of an observable in a many-body system, the repeated randomness assumption, which states that the system returns in a short time to a maximum entropy state, is a crucial hypothesis to guarantee that the effective dynamics is classical, Markovian and obeys local detailed balance. While the latter behaviour is frequently observed in naturally occurring processes, the repeated randomness assumption is in blatant contradiction to the microscopic reversibility of the system. Here, we show that the use of the repeated randomness assumption can be justified in the description of the effective dynamics of an observable that is both slow and coarse, two properties we will define rigorously. Then, our derivation will invoke essentially only the eigenstate thermalization hypothesis and typicality arguments. While the assumption of a slow observable is subtle, as it provides only a necessary but not sufficient condition, it also offers a unifying perspective applicable to, e.g., open systems as well as collective observables of many-body systems. All our ideas are numerically verified by studying density waves in spin chains.

quant-ph↗

arXiv2023

Characterization of random features of chaotic eigenfunctions in unperturbed basis

In this paper, we study random features manifested in components of energy eigenfunctions of quantum chaotic systems, given in the basis of unperturbed, integrable systems. Based on semiclassical analysis, particularly on Berry's conjecture, it is shown that the components in classically allowed regions can be regarded as Gaussian random numbers in certain sense, when appropriately rescaled with respect to the average shape of the eigenfunctions. This suggests that, when a perturbed system changes from integrable to chaotic, deviation of the distribution of rescaled components in classically allowed regions from the Gaussian distribution may be employed as a measure for the ``distance'' to quantum chaos. Numerical simulations performed in the LMG model and the Dicke model show that this deviation coincides with the deviation of the nearest-level-spacing distribution from the prediction of random-matrix theory. Similar numerical results are also obtained in two models without classical counterpart.

cond-mat.stat-mech↗

arXiv2022

Entanglement dynamics and classical complexity

We study the dynamical generation of entanglement for a two-body interacting system, starting from a separable coherent state. We show analytically that in the quasiclassical regime the entanglement growth rate can be simply computed by means of the underlying classical dynamics. Furthermore, this rate is given by the Kolmogorov-Sinai entropy, which characterizes dynamical complexity of classical motion. Our results, illustrated by numerical simulations on a model of coupled rotators, establish in the quasiclassical regime a link between the generation of entanglement, a purely quantum phenomenon, and classical complexity.

quant-ph↗

arXiv2022

Preferred basis derived from eigenstate thermalization hypothesis

We study the long-time average of the reduced density matrix (RDM) of an $m$-level central system, which is locally coupled to a large environment, under an overall Schrödinger evolution of the total system. We consider a class of interaction Hamiltonian, whose environmental part satisfies the so-called eigenstate thermalization hypothesis (ETH) ansatz with a constant diagonal part in the energy region concerned. On the eigenbasis of the central system's Hamiltonian, $\frac{1}{2}(m-1)(m+2)$ relations among elements of the averaged RDM are derived. When steady states exist, these relations imply the existence of a preferred basis, given by a renormalized Hamiltonian that includes certain averaged impact of the system-environment interaction. Numerical simulations performed for a qubit coupled to a defect Ising chain conform the analytical predictions.

quant-ph↗

arXiv2022

Eigenstate thermalization hypothesis and its deviations from random-matrix theory beyond the thermalization time

The Eigenstate Thermalization Hypothesis (ETH) explains emergence of the thermodynamic equilibrium by assuming a particular structure of observable's matrix elements in the energy eigenbasis. Schematically, it postulates that off-diagonal matrix elements are random numbers and the observables can be described by Random Matrix Theory (RMT). To what extent physical operators can be described by RMT, more precisely at which energy scale strict RMT description applies, is however not fully understood. We study this issue by introducing a novel numerical approach to probe correlations between matrix elements for Hilbert-space dimensions beyond those accessible for exact diagonalization. Our analysis is based on the evaluation of higher moments of operator submatrices, defined within energy windows of varying width. Considering nonintegrable quantum spin chains, we observe that genuine RMT behavior is absent even for narrow energy windows corresponding to time scales of the order of thermalization time $τ_\text{th}$ of the respective observables. We also demonstrate that residual correlations between matrix elements are reflected in the dynamics of out-of-time-ordered correlation functions.

cond-mat.stat-mech↗

arXiv2022

Stability of Exponentially Damped Oscillations under Perturbations of the Mori-Chain

There is an abundance of evidence that some relaxation dynamics, e.g., exponential decays, are much more common in nature than others. Recently, there have been attempts to trace this dominance back to a certain stability of the prevalent dynamics versus generic Hamiltonian perturbations. In the paper at hand, we tackle this stability issue from yet another angle, namely in the framework of the recursion method. We investigate the behavior of various relaxation dynamics with respect to alterations of the so-called Lanczos coefficients. All considered scenarios are set up in order to comply with the "universal operator growth hypothesis". Our numerical experiments suggest the existence of stability in a larger class of relaxation dynamics consisting of exponentially damped oscillations. Further, we propose a criterion to identify "pathological" perturbations that lead to uncommon dynamics.

quant-ph↗

arXiv2022

Numerically Probing the Universal Operator Growth Hypothesis

Recently, a hypothesis on the complexity growth of unitarily evolving operators was presented. This hypothesis states that in generic, non-integrable many-body systems the so-called Lanczos coefficients associated with an autocorrelation function grow asymptotically linear, with a logarithmic correction in one-dimensional systems. In contrast, the growth is expected to be slower in integrable or free models. In the paper at hand, we numerically test this hypothesis for a variety of exemplary systems, including 1d and 2d Ising models as well as 1d Heisenberg models. While we find the hypothesis to be practically fulfilled for all considered Ising models, the onset of the hypothesized universal behavior could not be observed in the attainable numerical data for the Heisenberg model. The proposed linear bound on operator growth eventually stems from geometric arguments involving the locality of the Hamiltonian as well as the lattice configuration. We investigate such a geometric bound and find that it is not sharply achieved for any considered model.

cond-mat.stat-mech↗

arXiv2022

Statistical and dynamical properties of the quantum triangle map

We study the statistical and dynamical properties of the quantum triangle map, whose classical counterpart can exhibit ergodic and mixing dynamics, but is never chaotic. Numerical results show that ergodicity is a sufficient condition for spectrum and eigenfunctions to follow the prediction of Random Matrix Theory, even though the underlying classical dynamics is not chaotic. On the other hand, dynamical quantities such as the out-of-time-ordered correlator (OTOC) and the number of harmonics, exhibit a growth rate vanishing in the semiclassical limit, in agreement with the fact that classical dynamics has zero Lyapunov exponent. Our finding show that, while spectral statistics can be used to detect ergodicity, OTOC and number of harmonics are diagnostics of chaos.

nlin.CD↗