Many-body localization, thermalization, and entanglement

TL;DR

This paper reviews recent theoretical and experimental progress in understanding many-body localization (MBL), a phenomenon where disordered quantum systems fail to thermalize, leading to unique entanglement and non-equilibrium properties.

Contribution

It provides a comprehensive overview of the theoretical framework of MBL, including quasi-local integrals of motion, and summarizes recent experimental observations across various platforms.

Findings

MBL systems do not thermalize and remain insulators at non-zero temperature.

Emergence of quasi-local integrals of motion explains the breakdown of thermalization.

Experimental signatures of MBL observed in ultracold atoms, trapped ions, and superconducting qubits.

Abstract

Thermalizing quantum systems are conventionally described by statistical mechanics at equilibrium. However, not all systems fall into this category, with many body localization providing a generic mechanism for thermalization to fail in strongly disordered systems. Many-body localized (MBL) systems remain perfect insulators at non-zero temperature, which do not thermalize and therefore cannot be described using statistical mechanics. In this Colloquium we review recent theoretical and experimental advances in studies of MBL systems, focusing on the new perspective provided by entanglement and non-equilibrium experimental probes such as quantum quenches. Theoretically, MBL systems exhibit a new kind of robust integrability: an extensive set of quasi-local integrals of motion emerges, which provides an intuitive explanation of the breakdown of thermalization. A description based on quasi-local integrals of motion is used to predict dynamical properties of MBL systems, such as the spreading of quantum entanglement, the behavior of local observables, and the response to external dissipative processes. Furthermore, MBL systems can exhibit eigenstate transitions and quantum orders forbidden in thermodynamic equilibrium. We outline the current theoretical understanding of the quantum-to-classical transition between many-body localized and ergodic phases, and anomalous transport in the vicinity of that transition. Experimentally, synthetic quantum systems, which are well-isolated from an external thermal reservoir, provide natural platforms for realizing the MBL phase. We review recent experiments with ultracold atoms, trapped ions, superconducting qubits, and quantum materials, in which different signatures of many-body localization have been observed. We conclude by listing outstanding challenges and promising future research directions.