Localisation on certain graphs with strongly correlated disorder

Abstract

Many-body localisation in interacting quantum systems can be cast as a disordered hopping problem on the underlying Fock-space graph. A crucial feature of the effective Fock-space disorder is that the Fock-space site energies are strongly correlated -- maximally so for sites separated by a finite distance on the graph. Motivated by this, and to understand the effect of such correlations more fundamentally, we study Anderson localisation on Cayley trees and random regular graphs, with maximally correlated disorder. Since such correlations suppress short distance fluctuations in the disorder potential, one might naively suppose they disfavour localisation. We find however that there exists an Anderson transition, and indeed that localisation is more robust in the sense that the critical disorder scales with graph connectivity $K$ as $\sqrt{K}$, in marked contrast to $K\ln K$ in the uncorrelated case. This scaling is argued to be intimately connected to the stability of many-body localisation. Our analysis centres on an exact recursive formulation for the local propagators as well as a self-consistent mean-field theory; with results corroborated using exact diagonalisation.

arXiv comment6 pages, 3 figures + supplementary (3 pages, 3 figures)

References in corpus (44)

• Many body localization and thermalization in quantum statistical mechanics
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Localization of interacting fermions at high temperature
• Many-body localization, thermalization, and entanglement
• The many-body localization phase transition
• Many-body localization edge in the random-field Heisenberg chain
• Interacting electrons in disordered wires: Anderson localization and low-temperature transport
• Many-body localization: an introduction and selected topics
• Quasiparticle Lifetime in a Finite System: A Non--Perturbative Approach
• Many-body localization in a disordered quantum Ising chain
• Theory of the many-body localization transition in one dimensional systems
• Universal properties of many-body delocalization transitions
• Anderson localization on the Bethe lattice: non-ergodicity of extended states
• Anderson localization on random regular graphs
• Analytically solvable renormalization group for the many-body localization transition
• Scaling theory of the Anderson transition in random graphs: ergodicity and universality
• Correlation-induced localization
• Many-body localization transition in a lattice model of interacting fermions: statistics of renormalized hoppings in configuration space
• Kosterlitz-Thouless scaling at many-body localization phase transitions
• Non-ergodic delocalized phase in Anderson model on Bethe lattice and regular graph
• Delocalized Glassy Dynamics and Many Body Localization
• The forward approximation as a mean field approximation for the Anderson and Many Body Localization transitions
• The Many-Body localization transition in the Hilbert space
• Renormalization-group study of the many-body localization transition in one dimension
• Critical behavior at the localization transition on random regular graphs
• Two critical localization lengths in the Anderson transition on random graphs
• Sub-diffusion in the Anderson model on random regular graph
• Many-body localization near the critical point
• Multifractality of wave functions on a Cayley tree: From root to leaves
• Fock-space correlations and the origins of many-body localisation
• Anderson transition on the Bethe lattice: an approach with real energies
• Many-body localization in Fock-space: a local perspective
• Percolation in Fock space as a proxy for many-body localisation
• Anderson Localization in 1D Systems with Correlated Disorder
• Anomalous dynamics in the ergodic side of the Many-Body Localization transition and the glassy phase of Directed Polymers in Random Media
• Self-consistent theory of many-body localisation in a quantum spin chain with long-range interactions
• Delocalization and ergodicity of the Anderson model on Bethe lattices
• Many Body Localization Due to Correlated Disorder in Fock Space
• Multifractal states in self-consistent theory of localization: analytical solution
• Anderson Localization on the Bethe Lattice using Cages and the Wegner Flow
• Exact solution of a percolation analogue for the many-body localisation transition
• Anderson localization in optical lattices with correlated disorder
• Simple probability distributions on a Fock-space lattice
• The Role of Power-Law Correlated Disorder in the Anderson Metal-Insulator Transition

Cited by in corpus (35)

• Many-Body Localization in the Age of Classical Computing
• Rare thermal bubbles at the many-body localization transition from the Fock space point of view
• From Anderson localization on Random Regular Graphs to Many-Body localization
• Critical properties of the Anderson transition in random graphs: two-parameter scaling theory, Kosterlitz-Thouless type flow and many-body localization
• Fock-space anatomy of eigenstates across the many-body localisation transition
• Test of Eigenstate Thermalization Hypothesis Based on Local Random Matrix Theory
• Self-consistent theory of mobility edges in quasiperiodic chains
• Anomalous multifractality in quantum chains with strongly correlated disorder
• Out of equilibrium Phase Diagram of the Quantum Random Energy Model
• Role of Fock-space correlations in many-body localization
• Diagnostics of nonergodic extended states and many body localization proximity effect through real-space and Fock-space excitations
• Ergodicity-to-localization transition on random regular graphs with large connectivity and in many-body quantum dots
• The Fock-space landscape of many-body localisation
• Statistics of systemwide correlations in the random-field XXZ chain: Importance of rare events in the many-body localized phase
• The connection between Hilbert-space return probability and real-space autocorrelations in quantum spin chains
• Localisation in quasiperiodic chains: a theory based on convergence of local propagators
• Anderson localization of composite particles
• Finite-size prethermalization at the chaos-to-integrable crossover
• Critical dynamics of long-range quantum disordered systems
• Effects of auto-correlated disorder on the dynamics in the vicinity of the many-body localization transition
• How periodic driving stabilises and destabilises Anderson localisation on random trees
• Many-body localized to ergodic transitions in a system with correlated disorder
• Quantum logarithmic multifractality
• Two-dimensional quantum breakdown model with Krylov subspace many-body localization
• Anatomy of localisation protected quantum order on Hilbert space
• Multifractality in high-dimensional graphs induced by correlated radial disorder
• Many-body critical phase in a quasiperiodic chain and dynamical Widom lines in Fock space properties
• Memory efficient Fock-space recursion scheme for computing many-fermion resolvents
• Krylov-space anatomy and spread complexity of a disordered quantum spin chain
• 2D Anderson Localization and KPZ sub-Universality Classes : sensitivity to boundary conditions and insensitivity to symmetry classes
• Critical Dynamics of the Anderson Transition on Small-World Graphs
• Large deviations in the many-body localization transition: The case of the random-field XXZ chain
• Anderson Localization on Husimi Trees and its implications for Many-Body localization
• Universal fluctuations of localized two interacting particles in one dimension
• Local density of states and scattering rates across the many-body localization transition