Thermalization Universality-Class Transition Induced by Anderson Localization

Weihua Zhang, Gabriel M. Lando, Barbara Dietz, Sergej Flach
Nonlinear Sciences, Chaotic Dynamics, Chaotic Dynamics (nlin.CD)
2023-08-16 16:00:00
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 breaks this invariance and Anderson localization emerges at the very limit. 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.
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