论文标题
通过相关表征多体定位过渡
Characterizing the many-body localization transition through correlations
论文作者
论文摘要
封闭的，相互作用的量子系统有可能在存在足够强的障碍的情况下过渡到多体局部（MBL）相，因此破坏了牙齿的性能并无法热化。在这项工作中，我们研究了整个Ergodic-MBL相图的相关性分布。我们发现MBL相衰减中的典型相关性是一个拉伸指数，范围$ r $最终越过了MBL相中的指数衰减。在过渡时，拉伸指数为$ e^{ - a \ sqrt {r}} $，一种让人联想到随机单元相位的衰减。虽然$ \ log（QMI）$的标准偏差具有范围依赖性，但$ \ log（QMI）$在过渡时在所有其他时刻（即偏斜及更高）收敛到范围不变的分布。这些分布的普遍性质提供了与Ergodic和MBL现象不同的转变的不同现象学。除了典型的相关性外，我们还研究了系统中的极端相关性，发现强远程相关性的概率在过渡时是最大的，这表明那里的谐振扩散。最后，我们分析了单个信息在系统的两半中共享一位信息的可能性，发现这种概率在MBL相中的深度不是零，但在中度疾病中消失了，远高于过渡。
Closed, interacting, quantum systems have the potential to transition to a many-body localized (MBL) phase under the presence of sufficiently strong disorder, hence breaking ergodicity and failing to thermalize. In this work we study the distribution of correlations throughout the ergodic-MBL phase diagram. We find the typical correlations in the MBL phase decay as a stretched exponential with range $r$ eventually crossing over to an exponential decay deep in the MBL phase. At the transition, the stretched exponential goes as $e^{-A\sqrt{r}}$, a decay that is reminiscent of the random singlet phase. While the standard deviation of the $\log(QMI)$ has a range dependence, the $\log(QMI)$ converges to a range-invariant distribution on all other moments (i.e., the skewness and higher) at the transition. The universal nature of these distributions provides distinct phenomenology of the transition different from both the ergodic and MBL phenomenologies. In addition to the typical correlations, we study the extreme correlations in the system, finding that the probability of strong long-range correlations is maximal at the transition, suggesting the proliferation of resonances there. Finally, we analyze the probability that a single bit of information is shared across two halves of a system, finding that this probability is non-zero deep in the MBL phase but vanishes at moderate disorder well above the transition.
