From localization in quenched disorder to new forms of many-body localization

近年来，人们在理论和实验上都做出了大量努力来理解量子热化：封闭的量子系统在么正动力学下演化，如何达到热平衡状态的问题。热化被认为是根据本征态热化假说(ETH)来描述的。据此，热化哈密顿量的每个本征态本质上就像一个热系综，就局域可观测量的期望值而言。鉴于其普遍性，人们对违反ETH的系统非常感兴趣。两个著名的例子是微调可积系统和多体定域(MBL)相，它发生在存在强烈无序的情况下。最近，人们发现了导致非遍历行为的新机制，包括动力学约束模型(KCM)，例如在Rydberg链中实现的模型，以及格点规范理论(LGT)中的无序局域化。在这个项目中，我们将推出新的工具来刻画无序系统中的MBL，并研究不同的遍历破坏机制之间的相互作用。首先，我们将探索费米子和玻色子系统中的多量子发光，重点放在一体论的观点上，特别是考虑到密度的分析。一方面，我们将使用实验上可获得的一体化测量和快照数据来表征MBL阶段以及MBL转变。另一方面，我们将在前人工作的基础上，研究单体近似，以有效地研究强无序和弱相互作用区域中MBL系统的动力学性质，并进一步发展这些方法来研究玻色子。第二，我们将研究晶格系统中强倾斜光场中原子相互作用的物理学。一个纯线性场导致了一个有效的具有约束动力学的偶极守恒模型，而这反过来又导致了一维中的希尔伯特空间碎裂和慢动力学。我们将把这个概念推广到2D系统，并包含高阶矩守恒。第三，我们将研究在约束模型中猝灭无序的影响，并研究动力学约束系统向MBL相的转变。第四，我们将仔细研究在D&GT；1维分形系统中稳定MBL的可能性。虽然稀有区域预计会破坏一般D&>1维系统中的MBL的稳定性，但零散的希尔伯特空间可能会提供一种可行的方法来避免MBL的崩溃。

Recent years have seen a great deal of effort —both theoretical and experimental— to understand quantum thermalization: the question of how closed quantum systems, evolving under unitary dynamics, reach a state of thermal equilibrium. Thermalization is believed to be characterized in terms of the Eigenstate Thermalization Hypothesis (ETH). According to this, each eigenstate of a thermalizing Hamiltonian essentially behaves like a thermal ensemble as far as expectation values of local observables are concerned. Given its generality, there has been much interest in systems that violate ETH. Two well-known instances are fine-tuned integrable systems and the many-body localized (MBL) phase, which occurs in the presence of strong disorder. More recently, new mechanisms have been discovered that lead to non-ergodic behavior, including kinetically constrained models (KCMs), as realized for example in Rydberg chains, and disorder free localization in lattice gauge theories (LGT). In this project, we will derive new tools to characterize MBL in disordered systems and investigate the interplay between different ergodicity breaking mechanisms. First, we will explore MBL in fermionic and bosonic systems with a focus on the one-body point of view, in particular, considering the analysis of densities. On the one hand, we will use experimentally accessible one-body measures and snapshot data to characterize the MBL phase as well as the MBL transition. On the other hand, we will build upon previous work and investigate one-body approximations to efficiently study the dynamical properties of MBL systems in the regime of strong disorder and weak interactions and further develop these approaches for bosons. Second, we will study the physics of interacting atoms in strong tilted fields in lattice systems. A purely linear field leads to an effective dipole-conserving model with constrained dynamics that in turn has shown to give rise to Hilbert-space fragmentation and slow dynamics in 1D. We will extend this concept to 2D systems and include higher-order moment conservations. Third, we will investigate the effect of quenched disorder in constrained models and investigate the transition into an MBL phase for kinetically constrained systems. Fourth, we will scrutinize the possibility to stabilize MBL in D > 1 dimensional fractonic systems. While rare regions are expected to destabilize MBL in generic D > 1 dimensional systems, the fragmented Hilbert space might provide a viable way to avoid a collapse of MBL.