Thermalization Universality-Class Transition Induced by Anderson Localization

TL;DR

This paper investigates how disorder-induced Anderson localization causes a transition between two universality classes of thermalization slowdown in classical circuits, revealing a link between localization length and system dynamics.

Contribution

It demonstrates that tuning disorder and nonlinearity induces a crossover from long-range to short-range thermalization classes, connecting Anderson localization with universality class transitions.

Findings

Lyapunov spectra differ markedly near integrability.

Disorder triggers a transition from long-range to short-range class.

Lyapunov spectrum becomes exponentially suppressed with localization.

Abstract

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, $\xi$, from $\xi \approx N$ to $\xi \ll N$, 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.