Thouless Energy Challenges Thermalization on the Ergodic Side of the Many-Body Localization Transition
arXiv:2001.03990 · doi:10.1103/PhysRevB.102.014201
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.
arXiv comment14 pages, 9 figures. Accepted preprint; to appear in Phys. Rev. B
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