标题： 通过奇异值分解诊断非厄米多体局域化和量子混沌 显示英文标题

标题： Diagnosing non-Hermitian Many-Body Localization and Quantum Chaos via Singular Value Decomposition

摘要： 强局域无序在相互作用的量子自旋链中可以将扩展的本征模转化为局域的本征态，从而产生多体局域（MBL）相。 这伴随着不同的谱统计特性：扩展相具有混沌特性，而局域相具有可积性。 在孤立系统中，局域化和混沌是通过本征值、本征矢量和实时动力学之间的关系网络来定义的。 当系统变为开放系统时，这些关系可能会发生变化。 我们询问，随机耗散（不带随机无序）是否可以在原本可积的系统中诱导出混沌或局域行为。 耗散通过非厄米哈密顿量来描述，这些哈密顿量可以通过对零测量进行条件化的马尔可夫动力学有效获得。 通过使用奇异值分解以及引入新的诊断工具，这些工具补充了奇异值统计，即奇异形式因子、逆参与比率和奇异矢量的纠缠熵，我们提供了肯定的答案。 我们的方法在具有随机局域耗散的XXZ哈密顿量中进行了说明。 显示英文摘要

摘要： Strong local disorder in interacting quantum spin chains can turn delocalized eigenmodes into localized eigenstates, giving rise to many-body localized (MBL) phases. This is accompanied by distinct spectral statistics: chaotic for the delocalized phase and integrable for the localized phase. In isolated systems, localization and chaos are defined through a web of relations among eigenvalues, eigenvectors, and real-time dynamics. These may change as the system is made open. We ask whether random dissipation (without random disorder) can induce chaotic or localized behavior in an otherwise integrable system. The dissipation is described using non-Hermitian Hamiltonians, which can effectively be obtained from Markovian dynamics conditioned on null measurement. Through the use of the singular value decomposition and the introduction of new diagnostic tools complementing the singular-value statistics, namely, the singular form factor, the inverse participation ratio, and entanglement entropy for singular vectors, we provide a positive answer. Our method is illustrated in an XXZ Hamiltonian with random local dissipation.