有迁移率边的一维准周期势系统中多体局域化的研究

In this work we aim to study the many-body localization (MBL) transition in one-dimensional quasiperiodic systems. Studies on MBL dated back to P. W. Anderson’s seminal work in 1958, in which he showed that isolated (noninteracting) quantum systems can become completely localized if the disorder strengths are strong enough. Since then, quantum localization has always been the central paradigm of condensed matter physics. Recently people realized that Anderson localization is actually stable against finite local interactions, which thus established quantum localization in a many-body system (now known as many-body localization) as a stable dynamical phase of matter. This phase is extremely important because it is the only known robust mechanism to avoid thermalization in a closed system, and thus has potential applications in quantum information storage, new dynamical phases of matter, etc. In the past decade most studies on MBL were focused on systems with quenched disorder, which is rather difficult to implement in the experiment. Instead, most MBL experiments to date focused on quasiperiodic systems, which can be created using two laser beams with incommensurate wave vectors. In this work, we study the MBL transition in this type of quasiperiodic systems. In particular, we want to understand how the existence of a single-particle mobility edge (i.e., a coexistence of extended and localized states in the single-particle energy spectrum) could affect the MBL transition. Our work will deepen our understanding on quantum thermalization in an isolated system and possibility lead to progress in various aspects of quantum information theory including quantum information storage and quantum scrambling in an isolated system.

本项目拟研究一维准周期势系统中多体局域化相变的问题。多体局域化最早可以追溯到安德森局域化的工作。该工作指出，随着无序度的增加，一个孤立量子系统可能会出现从延展态到局域化相变。这个问题近年来得到极大的发展，因为研究发现这个无相互作用极限下的相变在引入短程相互作用之后仍然是稳定的。这就意味着一个孤立的多体系统中可以存在一个稳定的无法达到热力学平衡态的动力学相。这样的一个新奇物相引起了学界极大的兴趣，也是目前理论凝聚态方向最重要的研究热点之一。但是目前大多数关于多体局域化的研究都集中在无序系统中，而无序系统在实验上是很难实现的。本项目的出发点就是近年来多体局域化实验中很常用的一维准周期势系统。这样的系统与一维无序系统有着很大区别，比如可以存在迁移率边。我们希望研究的就是迁移率边的存在如何影响多体局域化的相变。这个研究将会极大地增进我们对于孤立量子系统中的热力学平衡的本质以及量子信息存储的理解。

本项目围绕着有单粒子迁移率边的一维准周期势系统中多体局域化的问题展开了系统性的理论研究，完成了《计划任务书》中的研究计划，取得了重要的理论研究成果。本项目的研究内容可以划分为以下四个方面：(1) 一维准周期系统中单粒子迁移率边的性质；(2) 单粒子迁移率边的存在对多体局域化的影响；(3) 杂质对于量子多体疤痕态的影响；(4) 二维摩尔体系中的输运性质。本项目为实验上研究一维准周期系统中单粒子迁移率边提供了全新的可能性，并系统性地研究了单粒子迁移率边对于多体局域化现象的影响。