Localization and chaos in a spin glass model with random fields: Mapping to the localization problem in a Bethe lattice with a correlated disorder

Abstract

The analytical solution of a many-body localization problem in a quantum Sherrington-Kirkpatrick spin glass model in a random longitudinal field is proposed matching the problem with a model of Anderson localization in a Bethe lattice. The localization transition is dramatically sensitive to the relationship between interspin interaction and random field revealing different regimes in which the interaction can either suppress or enhance the delocalization. The localization is enhanced by decreasing the temperature and the localization transition shows a remarkable universality in a spin glass phase. The observed trends should be qualitatively relevant for other systems showing many-body localization.

15 pages, 5 figures, Revised version, accepted by Annalen der Physik for publication in the Special Issue dedicated to Many Body Localization

References in corpus (11)

• Many body localization and thermalization in quantum statistical mechanics
• Phenomenology of fully many-body-localized systems
• Many-body localization in periodically driven systems
• Integrals of motion in the Many-Body localized phase
• Interferometric probes of many-body localization
• Many-body mobility edge in a mean-field quantum spin glass
• Many-Body Delocalization in Strongly Disordered System with Long-Range Interactions: Finite Size Scaling
• Localized systems coupled to small baths: from A${}_{nderson}$ to Z${}_{eno}$
• Dimensional dependence of the metal-insulator transition
• Minimal Fokker-Planck theory for the thermalization of mesoscopic subsystems
• Local field distributions in spin glasses

Cited by in corpus (20)

• Many-body localization: an introduction and selected topics
• Can many-body localization persist in the presence of long-range interactions or long-range hopping?
• Fock-space correlations and the origins of many-body localisation
• Thermal inclusions: how one spin can destroy a many-body localized phase
• Spectral diffusion and scaling of many-body delocalization transitions
• Non-ergodic delocalized phase with Poisson level statistics
• Quantum chaos and ensemble inequivalence of quantum long-range Ising chains
• Many-body localization in spin chains with the long-range transverse interactions: scaling of critical disorder with the system size
• Slow Nonthermalizing Dynamics in a Quantum Spin Glass
• Many body localization-delocalization transition in quantum Sherrington-Kirkpatrick model
• Phase Diagram of the Quantum Random Energy Model
• The Fock-space landscape of many-body localisation
• Chaotic dynamics in a quantum Fermi-Pasta-Ulam problem
• Spectral Analysis of the Quantum Random Energy Model
• Comment on "Many-body localization in Ising models with random long-range interactions"
• Generalized Random Energy Models in a Transversal Magnetic Field: Free Energy and Phase Diagrams
• Investigating finite-size effects in random matrices by counting resonances
• Quantum glass of interacting bosons with off-diagonal disorder
• Stability of quasicrystalline ultracold fermions to dipolar interactions
• Traveling/non-traveling phase transition and non-ergodic properties in the random transverse-field Ising model on the Cayley tree