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  • Letter
  • Open Access

Thermalization universality-class transition induced by Anderson localization

Weihua Zhang1,2,*, Gabriel M. Lando1,†, Barbara Dietz1,3,‡, and Sergej Flach1,3,§

  • 1Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon 34126, Republic of Korea
  • 2Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China
  • 3Basic Science Program, Korea University of Science and Technology, Daejeon 34113, Republic of Korea

  • *zhangwh2018@gmail.com
  • †gmlando@ibs.re.kr
  • ‡bdietzp@gmail.com
  • §sergejflach@googlemail.com
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Phys. Rev. Research 6, L012064 – Published 25 March, 2024

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

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-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 ξ from ξ≈N to ξ≪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.

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Phys. Rev. Research 6, L012064– Published 25 March, 2024
  • Received 30 August 2023
  • Revised 30 November 2023
  • Accepted 10 March 2024
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