Density correlations and transport in models of many-body localization

Abstract

We present a review of recent theoretical results concerning the many-body localization (MBL) phenomenon, with the emphasis on dynamical density correlations and transport quantities. They are shown to be closely related, providing a comprehensive description of the ergodic-to-nonergodic transition, consistent with experimental findings. While the focus is set mostly on the one-dimensional model of interacting spinless fermions, we also present evidence for the absence of full MBL in the one-dimensional Hubbard model and for the density-wave decay induced by the inter-chain coupling.

Feature Article of the special issue Annalen der Physik: "Many-Body Localization"

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Cited by in corpus (42)

• Many-body localization: an introduction and selected topics
• Quantum chaos challenges many-body localization
• Recent progress in many-body localization
• Probing Slow Relaxation and Many-Body Localization in Two-Dimensional Quasi-Periodic Systems
• Thouless energy and multifractality across the many-body localization transition
• Many-Body Localization in the Age of Classical Computing
• Slow dynamics and strong finite-size effects in many-body localization with random and quasi-periodic potential
• Dynamics and Transport at the Threshold of Many-Body Localization
• Self-consistent approach to many-body localization and subdiffusion
• A self-consistent Hartree-Fock approach to Many-Body Localization
• The internal clock of many-body delocalization
• Quantum coherence and the localization transition
• Self-averaging in many-body quantum systems out of equilibrium. II. Approach to the localized phase
• Mobility edge in long-range interacting many-body localized systems
• Decay of spin-spin correlations in disordered quantum and classical spin chains
• Identification of Majorana Modes in Interacting Systems by Local Integrals of Motion
• Magnetization dynamics in clean and disordered spin-1 XXZ chains
• Reduced-basis approach to many-body localization
• Transient and persistent particle subdiffusion in a disordered chain coupled to bosons
• Relaxation at different length-scales in models of many-body localization
• Coexistence of diffusive and ballistic transport in integrable quantum lattice models
• Many-body localization as a percolation phenomenon
• Strong Disorder Real-Space Renormalization for the Many-Body-Localized phase of random Majorana models
• Diffusion in the Anderson model in higher dimensions
• Slow diffusion and Thouless localization criterion in modulated spin chains
• Emergent dipole moment conservation and subdiffusion in tilted chains
• Dynamics of the one-dimensional Anderson insulator coupled to various bosonic baths
• Sudden removal of a static force in a disordered system: Induced dynamics, thermalization, and transport
• Out-of-time-ordered measurements as a probe of quantum dynamics
• Random Transverse Field Spin-Glass Model on the Cayley tree : phase transition between the two Many-Body-Localized Phases
• Statistics of systemwide correlations in the random-field XXZ chain: Importance of rare events in the many-body localized phase
• Tower of two-dimensional scar states in a localized system
• Strong Disorder Renormalization for the dynamics of Many-Body-Localized systems : iterative elimination of the fastest degree of freedom via the Floquet expansion
• Strongly disordered Anderson insulator chains with generic two-body interaction
• Resistivity and its fluctuations in disordered many-body systems: from chains to planes
• Finite-size prethermalization at the chaos-to-integrable crossover
• Many-Body-Localization : Strong Disorder perturbative approach for the Local Integrals of Motion
• Cat states carrying long-range correlations in the many-body localized phase
• Even and odd normalized zero modes in random interacting Majorana models respecting the Parity $P$ and the Time-Reversal-Symmetry $T$
• Scaling of many-body localization transitions: Quantum dynamics in Fock space and real space
• Construction of Many-Body-Localized Models where all the eigenstates are Matrix-Product-States
• Spin and energy diffusion vs. subdiffusion in disordered spin chains