Corps, Angel L.Molina, Rafael A.Relaño Pérez, Armando2023-06-162023-06-162020-07-012469-995010.1103/PhysRevB.102.014201https://hdl.handle.net/20.500.14352/6420©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.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.engjournal articlehttps://doi.org/10.1103/PhysRevB.102.014201https://journals.aps.org/open access536Statistical-mechanicsQuantumRepulsionBehaviorSpectraSystemsChaosTermodinámica2213 Termodinámica