Publication: Thouless energy challenges thermalization on the ergodic side of the many-body localization transition
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2020-07-01
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American Physical Society
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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 nonmonotonically, exhibiting a strong peak at an intermediate value of the disorder. Furthermore, we show that nonthermalizing 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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©2020 American Physical Society. This work has been supported by the Spanish Grants No. FIS2015-63770-P (MINECO/FEDER) and No. PGC2018-094180-B-I00 (MCIU/AEI/FEDER, EU), CAM/FEDER Project No. S2018/TCS-4342 (QUITEMAD-CM), and CSIC Research Platform No. PTI-001.