Mobility Edge in the Anderson model on partially disordered random regular graphs

Abstract

In this Letter we study numerically the Anderson model on partially disordered random regular graphs (RRG) considered as the toy model for a Hilbert space of interacting disordered many-body system. The protected subsector of zero-energy states in a many-body system corresponds to clean nodes in RRG ensemble. Using adjacent gap ratio statistics and IPR we find the sharp mobility edge in the spectrum of one-particle Anderson model above some critical density of clean nodes. Its position in the spectrum is almost independent on the disorder strength. The possible application of our result for the controversial issue of mobility edge in the many-body localized (MBL) phase is discussed.

References in corpus (46)

• Many body localization and thermalization in quantum statistical mechanics
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Many-body localization, thermalization, and entanglement
• Many-body localization edge in the random-field Heisenberg chain
• Quantum many-body scars
• Quasiparticle Lifetime in a Finite System: A Non--Perturbative Approach
• Many-body localization: an introduction and selected topics
• Quantum Many-Body Scars and Weak Breaking of Ergodicity
• Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
• Quantum scarred eigenstates in a Rydberg atom chain: entanglement, breakdown of thermalization, and stability to perturbations
• Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis
• Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain
• Anderson localization on the Bethe lattice: non-ergodicity of extended states
• Observation of many-body localization in a one-dimensional system with single-particle mobility edge
• Many-body delocalization as a quantum avalanche
• Anderson localization on random regular graphs
• Absence of many-body mobility edges
• Many Body Scars as a Group Invariant Sector of Hilbert Space
• Scaling theory of the Anderson transition in random graphs: ergodicity and universality
• Fractality of wave functions on a Cayley tree: Difference between a tree and a locally tree-like graph without boundary
• 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
• Non-ergodic delocalized phase in Anderson model on Bethe lattice and regular graph
• From tunnels to towers: quantum scars from Lie Algebras and q-deformed Lie Algebras
• Weak chaos in the disordered nonlinear Schroedinger chain: destruction of Anderson localization by Arnold diffusion
• Return probability for the Anderson model on the random regular graph
• Delocalized Glassy Dynamics and Many Body Localization
• The Many-Body localization transition in the Hilbert space
• Quasi-symmetry groups and many-body scar dynamics
• Dephasing and weak localization in disordered Luttinger liquid
• Topology vs. Anderson localization: non-perturbative solutions in one dimension
• Many-Body Spectral Reflection Symmetry and Protected Infinite-Temperature Degeneracy
• Eigenvalue tunnelling and decay of quenched random networks
• Anderson localization and the topology of classifying spaces
• Fock-space anatomy of eigenstates across the many-body localisation transition
• Finite size correction to the spectrum of regular random graphs: an analytical solution
• The fate of quantum many-body scars in the presence of disorder
• Area-law entangled eigenstates from nullspaces of local Hamiltonians
• Delocalization and ergodicity of the Anderson model on Bethe lattices
• Anderson transition and multifractals in the spectrum of the Dirac operator of Quantum Chromodynamics at high temperature
• Self-Assembly of Geometric Space from Random Graphs
• Many-body localization in Bose-Hubbard model: evidence for the mobility edge
• Localization of Dirac Fermions in Finite-Temperature Gauge Theory
• Stability of mobility edges in disordered interacting systems
• Interacting Thermofield Doubles and Critical Behavior in Random Regular Graphs
• Metal or Insulator? Dirac operator spectrum in holographic QCD

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• Ergodicity-to-localization transition on random regular graphs with large connectivity and in many-body quantum dots
• Anatomy of the fragmented Hilbert space: eigenvalue tunneling, quantum scars and localization in the perturbed random regular graph
• Robust extended states in Anderson model on partially disordered random regular graphs
• Scaling of many-body localization transitions: Quantum dynamics in Fock space and real space