Many-body chaos and anomalous diffusion across thermal phase transitions in two dimensions

Abstract

Chaos is an important characterization of classical dynamical systems. How is chaos linked to the long-time dynamics of collective modes across phases and phase transitions? We address this by studying chaos across Ising and Kosterlitz-Thouless transitions in classical XXZ model. We show that spatio-temporal chaotic properties have crossovers across the transitions and distinct temperature dependence in the high and low-temperature phases which show normal and anomalous diffusions, respectively. Our results also provide new insights into the dynamics of interacting quantum systems in the semiclassical limit.

Classical route to ergodicity and scarring in collective quantum systems

“…for details. The spatio-temporal growth of the decorrelator exhibiting a lightcone like spreading of the initial perturbation has also been observed for different spin models [169,[306][307][308] as well as in other manybody systems [309][310][311][312]. Apart from the OTOC, in the recent years, the dynamical behavior of the spectral form factor (SFF) has also been used for the diagnosis of 'many-body quantum chaos' [313][314][315][316].…”

Dynamical signatures of Chaos to integrability crossover in 2×2 generalized random matrix ensembles

“…(b) Temporal evolution of fidelity where Thouless and relaxation times are denoted by markers and correlation hole is marked by dotted lines. Pink bold line is the analytical form for GSE (table 4) and the dashed lines are fit using equation (25). The asymptotic values are given in table 2.…”

“…The WDE have two constraints: statistical independence of the matrix elements and canonical invariance [18]. We need to relax either or both of these constraints to capture the intermediate spectral properties found in the systems deviating from the conventional Boltzmann statistics [19][20][21][22][23][24][25]. A prominent random matrix model without canonical invariance is the Rosenzweig-Porter ensemble (RPE).…”

Robustness of Kardar-Parisi-Zhang scaling in a classical integrable spin chain with broken integrability

“…To do so, we compute the out-of-time-ordered correlator (OTOC) in the ipILLL model. The OTOC has recently been studied in several classical models as a diagnostic tool to probe how initially localized perturbations spread spatially and grow (or decay) temporally [27][28][29][30][31][32][33][34][35][36]. In order to compute the OTOC for the spin chains, we consider the following scheme.…”