Information-theoretic memory scaling in the many-body localization transition
Information-theoretic memory scaling in the many-body localization transition
复制标题
DOI：
10.1103/physrevb.105.205133
复制
发表时间：
2020-09
影响因子：
3.7
通讯作者：
Alexander Nico-Katz;A. Bayat;S. Bose
中科院分区：
文献类型：
--
作者：
Alexander Nico-Katz;A. Bayat;S. Bose
多体局部化阶段的一个关键特征是遍历性的破坏，从而出现局部记忆。随着时间的推移，信息被显示为本地保存。由于记忆必然是一个与时间相关的概念，因此一些现有的动力学量研究已经部分地捕捉到了它。然而，这些数量对于输入状态来说既不是最优的，也不是民主的；因此，在多体定位的背景下，对局部记忆的基本和完整的信息理论理解仍然难以实现。我们引入动态 Holevo 量作为局部记忆的真正量词，概述了它相对于其他量（例如不平衡或纠缠熵）的优势。我们发现在多体定位转换过程中其稳态具有清晰的缩放行为，并确定了捕获这种行为的二参数缩放模拟族。我们对该动态量进行全面的有限尺寸缩放分析，提取转变点和缩放指数。
A key feature of the many-body localized phase is the breaking of ergodicity and consequently the emergence of local memory; revealed as the local preservation of information over time. As memory is necessarily a time dependent concept, it has been partially captured by a few extant studies of dynamical quantities. However, these quantities are neither optimal, nor democratic with respect to input state; and as such a fundamental and complete information theoretic understanding of local memory in the context of many-body localization remains elusive. We introduce the dynamical Holevo quantity as the true quantifier of local memory, outlining its advantages over other quantities such as the imbalance or entanglement entropy. We find clear scaling behavior in its steady-state across the many-body localization transition, and determine a family of two-parameter scaling ansatze which captures this behavior. We perform a comprehensive finite size scaling analysis of this dynamical quantity extracting the transition point and scaling exponents.