Avalanches and many-body resonances in many-body localized systems
Avalanches and many-body resonances in many-body localized systems
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DOI：
10.1103/physrevb.105.174205
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发表时间：
2021-07
影响因子：
3.7
通讯作者：
A. Morningstar;Luis Colmenarez;V. Khemani;D. J. Luitz;D. Huse
中科院分区：
文献类型：
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作者：
A. Morningstar;Luis Colmenarez;V. Khemani;D. J. Luitz;D. Huse
本文对具有多体局域性的强无序自旋链中的雪崩不稳定性和多体共振进行了数值研究。我们区分了有限大小/时间MBL状态和渐近MBL阶段，并确定了MBL状态中的一些“标志”。我们的第一个里程碑是通过测量一端与无限槽耦合的有限链的最慢弛豫速率来估计MBL相在哪里变得不稳定。我们的估计表明，在无限长系统中，实际的MBL到热相变发生在MBL区，比大多数以前的研究表明的要深得多。我们的其他里程碑涉及系统范围的共鸣。我们发现产生具有全系统共振的特征态的有效矩阵元分布非常广泛。这意味着在典型的样品中，这种共振的开始发生在MBL区相当深的地方，并且第一次这样的共振通常涉及稀有的特征态对，它们的能量距离比最小间隙更远。因此，我们发现共振特性定义了两个标志，将MBL区划分为三个子区：(i)在最强无序时，典型样品不具有涉及系统范围多体共振的任何特征态；（ii）存在大量的中间状态，其中典型样本确实具有这种共振，但具有最小谱隙的特征态对没有；（iii）在随机性较弱的情况下，最小间隙涉及多体共振，因此受到水平排斥。然而，即使在这第三个子状态中，除了消失的部分特征态之外，所有特征态都保持非共振，因此系统在许多方面仍然表现为MBL。根据我们对雪崩不稳定性位置的估计，可能MBL阶段只是子区(i)的一部分。
We numerically study both the avalanche instability and many-body resonances in strongly-disordered spin chains exhibiting many-body localization (MBL). We distinguish between a finite-size/time MBL regime, and the asymptotic MBL phase, and identify some"landmarks"within the MBL regime. Our first landmark is an estimate of where the MBL phase becomes unstable to avalanches, obtained by measuring the slowest relaxation rate of a finite chain coupled to an infinite bath at one end. Our estimates indicate that the actual MBL-to-thermal phase transition, in infinite-length systems, occurs much deeper in the MBL regime than has been suggested by most previous studies. Our other landmarks involve system-wide resonances. We find that the effective matrix elements producing eigenstates with system-wide resonances are enormously broadly distributed. This means that the onset of such resonances in typical samples occurs quite deep in the MBL regime, and the first such resonances typically involve rare pairs of eigenstates that are farther apart in energy than the minimum gap. Thus we find that the resonance properties define two landmarks that divide the MBL regime in to three subregimes: (i) at strongest disorder, typical samples do not have any eigenstates that are involved in system-wide many-body resonances; (ii) there is a substantial intermediate regime where typical samples do have such resonances, but the pair of eigenstates with the minimum spectral gap does not; and (iii) in the weaker randomness regime, the minimum gap is involved in a many-body resonance and thus subject to level repulsion. Nevertheless, even in this third subregime, all but a vanishing fraction of eigenstates remain non-resonant and the system thus still appears MBL in many respects. Based on our estimates of the location of the avalanche instability, it might be that the MBL phase is only part of subregime (i).