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

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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.