Thermalization Universality-Class Transition Induced by Anderson Localization

Fuente: arXiv
Enregistré dans:
Détails bibliographiques
Auteurs principaux: Zhang, Weihua, Lando, Gabriel M., Dietz, Barbara, Flach, Sergej
Format: Preprint
Publié: 2023
Sujets:
Accès en ligne:
Tags: Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
_version_ 1866929290205986816
author Zhang, Weihua
Lando, Gabriel M.
Dietz, Barbara
Flach, Sergej
author_facet Zhang, Weihua
Lando, Gabriel M.
Dietz, Barbara
Flach, Sergej
contents We study the disorder-induced crossover between the two recently discovered thermalization slowing-down universality classes -- characterized by long- and short-range coupling -- in classical unitary circuits maps close to integrability. We compute Lyapunov spectra, which display qualitatively distinct features depending on whether the proximity to the integrable limit is short or long ranged. For sufficiently small nonlinearity, translationally invariant systems fall into the long-range class. Adding disorder to such a system triggers a transition to the short-range class -- implying a breaking of this invariance -- and in the very limit of vanishing non-linearity Anderson localization emerges. The crossover from long- to short-range class is attained by tuning the localization length, $ξ$, from $ξ\approx N$ to $ξ\ll N$, where $N$ is the system size. As a consequence, the Lyapunov spectrum becomes exponentially suppressed, depending on how strongly its translational invariance is destroyed. We expect that this disorder-induced crossover will lead to prethermalized phases and, following quantization, to many-body localization.
format Preprint
id arxiv_https___arxiv_org_abs_2308_08921
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Thermalization Universality-Class Transition Induced by Anderson Localization
Zhang, Weihua
Lando, Gabriel M.
Dietz, Barbara
Flach, Sergej
Chaotic Dynamics
We study the disorder-induced crossover between the two recently discovered thermalization slowing-down universality classes -- characterized by long- and short-range coupling -- in classical unitary circuits maps close to integrability. We compute Lyapunov spectra, which display qualitatively distinct features depending on whether the proximity to the integrable limit is short or long ranged. For sufficiently small nonlinearity, translationally invariant systems fall into the long-range class. Adding disorder to such a system triggers a transition to the short-range class -- implying a breaking of this invariance -- and in the very limit of vanishing non-linearity Anderson localization emerges. The crossover from long- to short-range class is attained by tuning the localization length, $ξ$, from $ξ\approx N$ to $ξ\ll N$, where $N$ is the system size. As a consequence, the Lyapunov spectrum becomes exponentially suppressed, depending on how strongly its translational invariance is destroyed. We expect that this disorder-induced crossover will lead to prethermalized phases and, following quantization, to many-body localization.
title Thermalization Universality-Class Transition Induced by Anderson Localization
topic Chaotic Dynamics
url https://arxiv.org/abs/2308.08921