Localization Bounds for Multiparticle Systems

Abstract

We consider the spectral and dynamical properties of quantum systems of $n$ particles on the lattice ${\mathbb{Z}}^d$, of arbitrary dimension, with a Hamiltonian which in addition to the kinetic term includes a random potential with iid values at the lattice sites and a finite-range interaction. Two basic parameters of the model are the strength of the disorder and the strength of the interparticle interaction. It is established here that for all $n$ there are regimes of high disorder, and/or weak enough interactions, for which the system exhibits spectral and dynamical localization. The localization is expressed through bounds on the transition amplitudes, which are uniform in time and decay exponentially in the Hausdorff distance in the configuration space. The results are derived through the analysis of fractional moments of the $n$-particle Green function, and related bounds on the eigenfunction correlators.

References in corpus (8)

• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Moment Analysis for Localization in Random Schroedinger Operators
• New characterizations of the region of complete localization for random Schrödinger operators
• An Invitation to Random Schroedinger operators
• Wegner bounds for a two-particle tight binding model
• Eigenfunctions in a two-particle Anderson tight binding model
• A Wegner estimate for multi-particle random Hamiltonians
• Anderson localisation for an interacting two-particle quantum system on $\mathbb{Z}$

Cited by in corpus (61)

• On Many-Body Localization for Quantum Spin Chains
• Localization protected quantum order
• Absence of diffusion in an interacting system of spinless fermions on a one-dimensional disordered lattice
• Many-body mobility edge in a mean-field quantum spin glass
• Dynamics of Many-Body Localization
• Anomalous Thouless energy and critical statistics on the metallic side of the many-body localization transition
• Entanglement spreading in a many-body localized system
• Quantum revivals and many-body localization
• The Nonlinear Schroedinger Equation with a random potential: Results and Puzzles
• Dynamical Localization in Disordered Quantum Spin Systems
• Multi-Particle Anderson Localisation: Induction on the Number of Particles
• Bringing order through disorder: Localization of errors in topological quantum memories
• Localization of Toric Code Defects
• Anomalous dynamics in the ergodic side of the Many-Body Localization transition and the glassy phase of Directed Polymers in Random Media
• Disorder-assisted error correction in Majorana chains
• The bootstrap multiscale analysis for the multi-particle Anderson model
• Induced Delocalization by Correlation and Interaction in the one-dimensional Anderson Model
• Quantum harmonic oscillator systems with disorder
• Low-energy Fock-space localization for attractive hard-core particles in disorder
• Multiparticle localization for disordered systems on continuous space via the fractional moment method
• Many-Body Localization in a finite-range Sachdev-Ye-Kitaev model
• On two-particle Anderson localization at low energies
• A uniform area law for the entanglement of eigenstates in the disordered XY chain
• Manifestations of dynamical localization in the disordered XXZ spin chain
• Random Field Induced Order in Low Dimension
• Hierarchy of many-body invariants and quantized magnetization in anomalous Floquet insulators
• Complete Dynamical Localization in Disordered Quantum Multi-Particle Systems
• Existence of the thermodynamic limit for disordered quantum Coulomb systems
• An Area Law for the Bipartite Entanglement of Disordered Oscillator Systems
• Eigenstate localization in a many-body quantum system
• Entanglement entropy of low-lying excitation in localized interacting system: Signature of Fock space delocalization
• Direct Scaling Analysis of localization in disordered systems. II. Multi-particle lattice systems
• Testing the universality of the many-body metal-insulator transition by time evolution of a disordered one-dimensional ultracold fermionic gas
• Bootstrap multiscale analysis and localization for multi-particle continuous Anderson Hamiltonians
• Localization in the Disordered Holstein model
• Exponential scaling limit of the single-particle Anderson model via adaptive feedback scaling
• Slow propagation in some disordered quantum spin chains
• Many-Body Localization: Concepts and Simple Models
• Characterization of the metal-insulator transport transition for the two-particle Anderson model
• Interaction-Induced Weakening of Localization in Few-Particle Disordered Heisenberg Chains
• Localization and IDS Regularity in the Disordered Hubbard Model within Hartree-Fock Theory
• Localization with Less Larmes: Simply MSA
• Universality of smoothness of Density of States in arbitrary higher-dimensional disorder under non-local interactions I. From Viéte--Euler identity to Anderson localization
• Localization in the random XXZ quantum spin chain
• Multiplicity theorem of singular Spectrum for general Anderson type Hamiltonian
• Many-body localization in the droplet spectrum of the random XXZ quantum spin chain
• Optimal Wegner estimate and the density of states for N-body, interacting Schrodinger operators with random potentials
• An Explicit Bound for Dynamical Localisation in an Interacting Many-Body System
• Multi-particle dynamical localization in a continuous Anderson model with an alloy-type potential
• Resonant tunneling in a system with correlated pure point spectrum
• The Existence of the Thermodynamic Limit for the System of Interacting Quantum Particles in Random Media
• An eigensystem approach to Anderson localization for multi-particle systems
• Anderson localization for two interacting quasiperiodic particles
• Decay of Complex-time Determinantal and Pfaffian\ Correlation Functionals in Lattices
• Multi-particle localization at low energy for the multi-dimensional continuous Anderson model
• Comprehensive proofs of localization in Anderson models with interaction. I. Two-particle localization estimates
• Anderson localization for a multi-particle model with alloy-type external potential
• Scaling Theory of Few-Particle Delocalization
• Lifshitz tails for the multi-particle continuous Anderson model
• Efficient localization bounds in a continuous multi-particle Anderson model with long-range interaction
• Efficient Anderson localization bounds for large multi-particle systems