Thouless Energy Challenges Thermalization on the Ergodic Side of the Many-Body Localization Transition

• URL: http://arxiv.org/abs/2001.03990v2
• Date: Sun, 21 Jun 2020 09:12:43 GMT
• Title: Thouless Energy Challenges Thermalization on the Ergodic Side of the Many-Body Localization Transition
• Authors: \'Angel L. Corps, Rafael A. Molina, and Armando Rela\~no
• Abstract summary: We study the ergodic side of the many-body localization transition in the disordered Heisenberg quantum spin chain. We show that the Thouless energy, extracted from long-range spectral statistics and the power-spectrum of the full momentum distribution fluctuations, is not large enough to guarantee thermalization.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the ergodic side of the many-body localization transition in its standard model, the disordered Heisenberg quantum spin chain. We show that the Thouless energy, extracted from long-range spectral statistics and the power-spectrum of the full momentum distribution fluctuations, is not large enough to guarantee thermalization. We find that both estimates coincide and behave non-monotonically, exhibiting a strong peak at an intermediate value of the disorder. Furthermore, we show that non-thermalizing initial conditions occur well within the ergodic phase with larger probability than expected. Finally, we propose a mechanism, driven by the Thouless energy and the presence of anomalous events, for the transition to the localized phase.

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