Ergodicity, Entanglement and Many-Body Localization

D. Abanin, E. Altman, I. Bloch, M. Serbyn, (2018).

Preprint | Published | English
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Abstract
Quantum systems of many particles, which satisfy the ergodicity hypothesis, are conventionally described by statistical mechanics. However, not all quantum systems are ergodic, with many-body localization providing a generic mechanism of ergodicity breaking by disorder. 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 ergodicity breaking mechanism. 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, quantum materials, and superconducting qubits, in which different signatures of many-body localization have been observed. We conclude by listing outstanding challenges and promising future research directions.
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Date Published
2018-05-01
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Cite this

Abanin D, Altman E, Bloch I, Serbyn M. Ergodicity, Entanglement and Many-Body Localization. 2018.
Abanin, D., Altman, E., Bloch, I., & Serbyn, M. (2018). Ergodicity, Entanglement and Many-Body Localization. ArXiv.
Abanin, Dmitry, Ehud Altman, Immanuel Bloch, and Maksym Serbyn. “Ergodicity, Entanglement and Many-Body Localization.” ArXiv, 2018.
D. Abanin, E. Altman, I. Bloch, and M. Serbyn, “Ergodicity, Entanglement and Many-Body Localization.” ArXiv, 2018.
Abanin D, Altman E, Bloch I, Serbyn M. 2018. Ergodicity, Entanglement and Many-Body Localization.
Abanin, Dmitry, et al. Ergodicity, Entanglement and Many-Body Localization. ArXiv, 2018.

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