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-circuit 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 range. 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 nonlinearity Anderson localization emerges. The crossover from the long- to the 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 the extent to which its translational invariance is destroyed. We expect that this disorder-induced crossover will lead to prethermalized phases and, following quantization, to many-body localization.

• Received 30 August 2023
• Revised 30 November 2023
• Accepted 10 March 2024

DOI:https://doi.org/10.1103/PhysRevResearch.6.L012064

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society