Recent progress in many-body localization

Abstract

This article is a brief introduction to the rapidly evolving field of many-body localization. Rather than giving an in-depth review of the subject, our aspiration here is simply to introduce the problem and its general context, outlining a few directions where notable progress has been achieved in recent years. We hope that this will prepare the readers for the more specialized articles appearing in the forthcoming dedicated volume of Annalen der Physik, where these developments are discussed in more detail.

Invited overview article for the Special Volume of Annalen der Physik on Many-Body Localization

References in corpus (27)

• Many-Body Physics with Ultracold Gases
• Thermalization and its mechanism for generic isolated quantum systems
• Localization of interacting fermions at high temperature
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Many-body localization edge in the random-field Heisenberg chain
• Many body localization in Heisenberg XXZ magnet in a random field
• Phenomenology of fully many-body-localized systems
• Equilibrium states of generic quantum systems subject to periodic driving
• Many-body localization in periodically driven systems
• Integrals of motion in the Many-Body localized phase
• Anomalous diffusion and Griffiths effects near the many-body localization transition
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• Periodically driven ergodic and many-body localized quantum systems
• Constructing local integrals of motion in the many-body localized phase
• Off-diagonal matrix elements of local operators in many-body quantum systems
• Quantum quenches in the many-body localized phase
• Eigenstate thermalization within isolated spin-chain systems
• Interferometric probes of many-body localization
• Non-ergodic phases in strongly disordered random regular graphs
• Dynamics in many-body localized quantum systems without disorder
• Quantum revivals and many-body localization
• Purification and many-body localization in cold atomic gases
• Scenario for delocalization in translation invariant systems
• Localized systems coupled to small baths: from A${}_{nderson}$ to Z${}_{eno}$
• Spectral tensor networks for many-body localization
• Explicit construction of local conserved operators in disordered many-body systems

Cited by in corpus (6)

• How a small quantum bath can thermalize long localized chains
• Time-dependent variational principle in matrix-product state manifolds: pitfalls and potential
• Transport properties across the many-body localization transition in quasiperiodic and random systems
• Absence of dynamical localization in interacting driven systems
• Entanglement renormalization for disordered systems
• A microscopically motivated renormalization scheme for the MBL/ETH transition