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00925njm 22002777a 4500 dc Corps, Angel L. author Molina, Rafael A. author Relaño Pérez, Armando author 2020-07-01 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. 2469-9950 10.1103/PhysRevB.102.014201 https://hdl.handle.net/20.500.14352/6420 https://doi.org/10.1103/PhysRevB.102.014201 https://journals.aps.org/ Thouless energy challenges thermalization on the ergodic side of the many-body localization transition