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.

中文翻译：

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在多体定位过渡的遍历侧，无穷无尽的挑战挑战了热化

我们在其标准模型无序的海森堡量子自旋链中研究了多体定位转变的遍历面。我们显示，从远程光谱统计数据和全动量分布波动的功率谱中提取的Thouless能量不足以保证热化。我们发现，这两个估计值均重合且表现为非单调，在该疾病的中间值处显示出很强的峰值。此外，我们表明非热化初始条件在遍历阶段内发生的可能性很大，且比预期的要大。最后，我们提出了一种由Thouless能量和异常事件的存在驱动的机制，用于过渡到局部阶段。