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了大量的努力来理解量子热化：在幺正动力学下演化的封闭量子系统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）来表征的。据此，热化哈密顿量的每一个本征态，就局部观测量的期望值而言，本质上表现为一个热系综。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局域（MBL）相，这发生在强无序的存在。最近，已经发现了导致非遍历行为的新机制，包括动力学约束模型（KCM），例如在里德伯链中实现的，以及格点规范理论（LGT）中的无无序局域化。在这个项目中，我们将获得新的工具来描述无序系统中的MBL，并研究不同遍历性破坏机制之间的相互作用。首先，我们将探讨在费米子和玻色子系统的MBL集中在一个身体的观点，特别是考虑到密度的分析。一方面，我们将使用实验上可访问的单体措施和快照数据来表征MBL相以及MBL过渡。另一方面，我们将建立在以前的工作和调查的单体近似，有效地研究MBL系统的动力学性质的制度，强无序和弱相互作用，并进一步发展这些方法的玻色子。其次，我们将研究晶格系统中强倾斜场中原子相互作用的物理。一个纯粹的线性场导致一个有效的偶极守恒模型与约束动力学，反过来又表明，引起希尔伯特空间碎片化和缓慢的动态在1D。我们将这个概念扩展到二维系统，包括高阶矩守恒。第三，我们将研究约束模型中淬火无序的影响，并研究动力学约束系统向MBL相的过渡。第四，我们将仔细研究在D > 1维分形系统中稳定MBL的可能性。虽然预计稀有区域会使一般D > 1维系统中的MBL不稳定，但碎片化的Hilbert空间可能提供了避免MBL崩溃的可行方法。

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.