Many-Body Localization and Thermalization in Quantum Statistical Mechanics

TLDR

Many‑body localized systems can retain local memory of initial conditions, making them candidates for quantum information storage. The paper reviews recent progress in the statistical mechanics of isolated quantum systems, focusing on quantum thermalization, the eigenstate thermalization hypothesis, and the phenomenology of many‑body localization. The authors examine many‑body Anderson‑localized systems that violate ETH, noting that their long‑time properties escape conventional ensembles, and they review the phenomenology of the MBL phase. Within the MBL phase, single‑eigenstate statistical mechanics uncovers dynamically stable ordered phases and phase transitions that are invisible to equilibrium statistical mechanics and can arise at high energy in low dimensions where equilibrium ordering is forbidden.

Abstract

We review some recent developments in the statistical mechanics of isolated quantum systems. We provide a brief introduction to quantum thermalization, paying particular attention to the eigenstate thermalization hypothesis (ETH) and the resulting single-eigenstate statistical mechanics. We then focus on a class of systems that fail to quantum thermalize and whose eigenstates violate the ETH: These are the many-body Anderson-localized systems; their long-time properties are not captured by the conventional ensembles of quantum statistical mechanics. These systems can forever locally remember information about their local initial conditions and are thus of interest for possibilities of storing quantum information. We discuss key features of many-body localization (MBL) and review a phenomenology of the MBL phase. Single-eigenstate statistical mechanics within the MBL phase reveal dynamically stable ordered phases, and phase transitions among them, that are invisible to equilibrium statistical mechanics and can occur at high energy and low spatial dimensionality, where equilibrium ordering is forbidden.