Torres-Herrera E J, Santos Lea F
Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apt. Postal J-48, Puebla 72570, Mexico.
Department of Physics, Yeshiva University, New York, NY 10016, USA
Philos Trans A Math Phys Eng Sci. 2017 Dec 13;375(2108). doi: 10.1098/rsta.2016.0434.
A main feature of a chaotic quantum system is a rigid spectrum where the levels do not cross. We discuss how the presence of level repulsion in lattice many-body quantum systems can be detected from the analysis of their time evolution instead of their energy spectra. This approach is advantageous to experiments that deal with dynamics, but have limited or no direct access to spectroscopy. Dynamical manifestations of avoided crossings occur at long times. They correspond to a drop, referred to as correlation hole, below the asymptotic value of the survival probability and to a bulge above the saturation point of the von Neumann entanglement entropy and the Shannon information entropy. By contrast, the evolution of these quantities at shorter times reflects the level of delocalization of the initial state, but not necessarily a rigid spectrum. The correlation hole is a general indicator of the integrable-chaos transition in disordered and clean models and as such can be used to detect the transition to the many-body localized phase in disordered interacting systems.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.
混沌量子系统的一个主要特征是其能级谱具有刚性，即能级不会交叉。我们讨论了如何通过分析晶格多体量子系统的时间演化而非其能谱，来检测能级排斥的存在。这种方法对于处理动力学问题但对光谱学的直接访问有限或无法直接访问光谱学的实验是有利的。避免交叉的动力学表现出现在长时间。它们对应于生存概率渐近值以下的下降，称为关联洞，以及冯·诺依曼纠缠熵和香农信息熵饱和点以上的凸起。相比之下，这些量在较短时间的演化反映了初始状态的离域化程度，但不一定反映刚性谱。关联洞是无序和清洁模型中可积 - 混沌转变的一般指标，因此可用于检测无序相互作用系统向多体局域相的转变。本文是主题为“量子系统中遍历性的崩溃：从固体到合成物质”的特刊的一部分。
