Bhakuni Devendra Singh, Sharma Auditya
Indian Institute of Science Education and Research, Bhopal, 462066, India.
J Phys Condens Matter. 2020 Jun 10;32(25):255603. doi: 10.1088/1361-648X/ab7c92.
Whether or not the thermodynamic entropy is equal to the entanglement entropy of an eigenstate is of fundamental interest, and is closely related to the eigenstate thermalization hypothesis (ETH). However, this has never been exploited as a diagnostic tool in many-body- localized (MBL) systems. In this work, we perform this diagnostic test on a clean interacting system (subjected to a static electric field) that exhibits three distinct phases: integrable, non-integrable ergodic and non-integrable MBL. We find that in the non-integrable phase, the equivalence between the thermodynamic entropy and the entanglement entropy of individual eigenstates holds. In sharp contrast, in the integrable and non-integrable MBL phases, the entanglement entropy shows large eigenstate-to-eigenstate fluctuations, and differs from the thermodynamic entropy. Thus the non-integrable MBL phase violates ETH similar to an integrable system; however, a key difference is that the magnitude of the entanglement entropy in the MBL phase is significantly smaller than in the integrable phase, where the entanglement entropy is of the same order of magnitude as in the non-integrable phase, but with a lot of eigenstate-to-eigenstate fluctuations. Quench dynamics from an initial CDW state independently supports the validity of the ETH in the ergodic phase and its violation in the MBL phase.
热力学熵是否等于本征态的纠缠熵是一个具有根本重要性的问题，并且与本征态热化假设（ETH）密切相关。然而，在多体局域化（MBL）系统中，这一点从未被用作一种诊断工具。在这项工作中，我们对一个纯净的相互作用系统（置于静电场中）进行了这种诊断测试，该系统呈现出三个不同的相：可积、不可积遍历和不可积MBL相。我们发现，在不可积相中，热力学熵与各个本征态的纠缠熵之间的等价关系成立。与之形成鲜明对比的是，在可积和不可积MBL相中，纠缠熵表现出很大的本征态间涨落，并且与热力学熵不同。因此，不可积MBL相类似于可积系统那样违反了ETH；然而，一个关键的区别在于，MBL相中的纠缠熵的大小明显小于可积相中的大小，在可积相中，纠缠熵与不可积相中的量级相同，但存在大量的本征态间涨落。从初始电荷密度波（CDW）态开始的猝灭动力学独立地支持了遍历相中ETH的有效性以及MBL相中ETH的违反情况。
