Localization in the random XXZ quantum spin chain
arXiv:2210.14873 · doi:10.1017/fms.2024.119
Abstract
We study the many-body localization (MBL) properties of the Heisenberg XXZ spin- chain in a random magnetic field. We prove that the system exhibits localization in any given energy interval at the bottom of the spectrum in a nontrivial region of the parameter space. This region, which includes weak interaction and strong disorder regimes, is independent of the size of the system and depends only on the energy interval. Our approach is based on the reformulation of the localization problem as an expression of quasi-locality for functions of the random many-body XXZ Hamiltonian. This allows us to extend the fractional moment method for proving localization, previously derived in a single-particle localization context, to the many-body setting.
arXiv comment32 pages, no figures
References in corpus (33)
- Many body localization and thermalization in quantum statistical mechanics
- Many-body localization, thermalization, and entanglement
- Observation of many-body localization of interacting fermions in a quasi-random optical lattice
- The many-body localization phase transition
- Many-body localization edge in the random-field Heisenberg chain
- Unbounded growth of entanglement in models of many-body localization
- Many body localization in Heisenberg XXZ magnet in a random field
- Many-body localization: an introduction and selected topics
- Probing entanglement in a many-body-localized system
- Anomalous diffusion and Griffiths effects near the many-body localization transition
- Avalanches and many-body resonances in many-body localized systems
- Thouless time analysis of Anderson and many-body localization transitions
- Dynamical obstruction to localization in a disordered spin chain
- Evidence for unbounded growth of the number entropy in many-body localized phases
- Absence of many-body mobility edges
- Challenges to observation of many-body localization
- Moment Analysis for Localization in Random Schroedinger Operators
- Localization Bounds for Multiparticle Systems
- Multi-Particle Anderson Localisation: Induction on the Number of Particles
- Many-body localization and mobility edge in a disordered Heisenberg spin ladder
- Localization Properties of the XY Spin Chain. A review of mathematical results with an eye toward Many-Body Localization
- Anderson localization for a class of models with a sign-indefinite single-site potential via fractional moment method
- The bootstrap multiscale analysis for the multi-particle Anderson model
- Multiscale Analysis and Localization of Random Operators
- Localization in interacting fermionic chains with quasi-random disorder
- Low-energy Fock-space localization for attractive hard-core particles in disorder
- Quantum harmonic oscillator systems with disorder
- Decay of correlations and absence of superfluidity in the disordered Tonks-Girardeau gas
- Manifestations of dynamical localization in the disordered XXZ spin chain
- Droplet States in the XXZ Heisenberg Chain
- Localization in an interacting quasi-periodic fermionic chain
- Slow propagation of information on the random XXZ quantum spin chain
- Localization and IDS Regularity in the Disordered Hubbard Model within Hartree-Fock Theory