Quantum coherence and the localization transition
Quantum coherence and the localization transition
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DOI：
10.1103/physrevb.100.224204
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发表时间：
2019-06
影响因子：
3.7
通讯作者：
Georgios Styliaris;Namit Anand;L. Venuti;P. Zanardi
中科院分区：
文献类型：
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作者：
Georgios Styliaris;Namit Anand;L. Venuti;P. Zanardi
量子系统中局域化的动态特征是缺乏输运，输运由构型空间状态相对于哈密顿本征基所具有的相干性控制。为了使这一观察更加精确，我们通过相干资源理论产生的量子相干测量来研究局域化转变。我们证明，逃逸概率（已知在遍历阶段和局部阶段表现出不同的行为）自然地作为相干性度量的平均值而出现。此外，利用主化理论，我们认为广泛的相干性度量家族可以检测转移矩阵（哈密顿量和配置基之间）的均匀性，从而充当定位的探针。我们为安德森和多体定位（MBL）提供了支持性的数字证据。对于哈密顿量的无穷小扰动，微分相干性定义了关联的黎曼度量。我们证明后者正是由动态电导率给出的，这是一个实验相关量，已知它在遍历阶段和多体局域阶段具有明显不同的行为。我们的结果表明，相干性的量子信息理论概念及其相关的几何结构可以为遍历-MBL 转变的难以捉摸的本质提供有用的见解。
A dynamical signature of localization in quantum systems is the absence of transport which is governed by the amount of coherence that configuration space states possess with respect to the Hamiltonian eigenbasis. To make this observation precise, we study the localization transition via quantum coherence measures arising from the resource theory of coherence. We show that the escape probability, which is known to show distinct behavior in the ergodic and localized phases, arises naturally as the average of a coherence measure. Moreover, using the theory of majorization, we argue that broad families of coherence measures can detect the uniformity of the transition matrix (between the Hamiltonian and configuration bases) and hence act as probes to localization. We provide supporting numerical evidence for Anderson and Many-Body Localization (MBL). For infinitesimal perturbations of the Hamiltonian, the differential coherence defines an associated Riemannian metric. We show that the latter is exactly given by the dynamical conductivity, a quantity of experimental relevance which is known to have a distinctively different behavior in the ergodic and in the many-body localized phases. Our results suggest that the quantum information-theoretic notion of coherence and its associated geometrical structures can provide useful insights into the elusive nature of the ergodic-MBL transition.