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 nonzero temperature, which do not thermalize and therefore cannot be described using statistical mechanics. This Colloquium reviews recent theoretical and experimental advances in studies of MBL systems, focusing on the new perspective provided by entanglement and nonequilibrium experimental probes such as quantum quenches. Theoretically, MBL systems exhibit a new kind of robust integrability: an extensive set of quasilocal integrals of motion emerges, which provides an intuitive explanation of the breakdown of thermalization. A description based on quasilocal 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. An outline is given of 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. Recent experiments with ultracold atoms, trapped ions, superconducting qubits, and quantum materials, in which different signatures of many-body localization have been observed, are reviewed. This Colloquium concludes by listing outstanding challenges and promising future research directions.

中文翻译：

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座谈会：多体定位，热化和纠缠

传统上，在平衡状态下通过统计力学来描述量子化热系统。但是，并非所有系统都属于此类，多体定位为热失控在严重混乱的系统中提供了一种通用机制。多体局部（MBL）系统在非零温度下仍是理想的绝缘体，不会发生热化，因此无法使用统计力学进行描述。这次座谈会回顾了MBL系统研究的最新理论和实验进展，重点介绍了纠缠和非平衡实验探针（例如量子猝灭）提供的新观点。从理论上讲，MBL系统表现出一种新型的鲁棒可积性：出现了一系列广泛的准局部运动积分，这提供了对热分解的直观解释。基于运动的准局部积分的描述用于预测MBL系统的动力学特性，例如量子纠缠的扩散，局部可观察物的行为以及对外部耗散过程的响应。此外，MBL系统可以表现出热力学平衡中禁止的本征态跃迁和量子级。概述了当前对多体局部和遍历相之间的量子-经典跃迁以及该跃迁附近的异常传输的理论理解。实验上，与外部储热库良好隔离的合成量子系统为实现MBL相提供了自然平台。最近对超冷原子，被困离子，审查了超导量子位和量子材料，其中观察到了多体定位的不同特征。本次研讨会的结尾列出了突出的挑战和有希望的未来研究方向。