论文标题
纠缠特征值的极端统计数据可以跟踪局部过渡的多体
Extremal statistics of entanglement eigenvalues can track the many-body localized to ergodic transition
论文作者
论文摘要
当猝灭障碍大于阈值时，一些相互作用的多体系统无法热化。尽管非零能量密度本征态（在多体谱的中间）的几种特性在这种多体定位（MBL）过渡过程中表现出了质的变化，但许多常用的诊断只能在广泛的过渡方案中进行。在这里，我们提供的证据表明，通过急剧定义的降低的子系统密度矩阵的极端特征值分布的变化，该过渡甚至可以精确地位于适度的系统大小上。特别是，我们的结果表明$ p* = \ lim_ {λ_2\ rightarrow \ ln（2）^{+}} p_2（λ_2）$，其中$ p_2（λ_2）$是第二个最低范围wittangelect eigenvalue $λ_2$的概率分布，是$λ_2$，$ pers $ priff us per* for py for p py for n''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' MBL相，而$ p* = 0 $在Ergodic阶段具有热化。因此，在MBL阶段中，仅通过一个子系统量子组的缠结，该子系统与系统的其余部分纠缠在一起存在非零的概率。相反，这种概率在热相中消失。
Some interacting disordered many-body systems are unable to thermalize when the quenched disorder becomes larger than a threshold value. Although several properties of nonzero energy density eigenstates (in the middle of the many-body spectrum) exhibit a qualitative change across this many-body localization (MBL) transition, many of the commonly-used diagnostics only do so over a broad transition regime. Here, we provide evidence that the transition can be located precisely even at modest system sizes by sharply-defined changes in the distribution of extremal eigenvalues of the reduced density matrix of subsystems. In particular, our results suggest that $p* = \lim_{λ_2 \rightarrow \ln(2)^{+}}P_2(λ_2)$, where $P_2(λ_2)$ is the probability distribution of the second lowest entanglement eigenvalue $λ_2$, behaves as an ''order-parameter'' for the MBL phase: $p*> 0$ in the MBL phase, while $p* = 0$ in the ergodic phase with thermalization. Thus, in the MBL phase, there is a nonzero probability that a subsystem is entangled with the rest of the system only via the entanglement of one subsystem qubit with degrees of freedom outside the region. In contrast, this probability vanishes in the thermal phase.
