<i>Colloquium</i>: Many-body localization, thermalization, and entanglement

Abstract

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

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Affiliated Institutions

• University of Geneva CH

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