A note on the quasiperiodic many-body localization transition in dimension $d>1$

Abstract

The nature of the many-body localization (MBL) transition and even the existence of the MBL phase in random many-body quantum systems have been actively debated in recent years. In spatial dimension $d>1$, there is some consensus that the MBL phase is unstable to rare thermal inclusions that can lead to an avalanche that thermalizes the whole system. In this note, we explore the possibility of MBL in quasiperiodic systems in dimension $d>1$. We argue that (i) the MBL phase is stable at strong enough quasiperiodic modulations for $d=2$, and (ii) the possibility of an avalanche strongly constrains the finite-size scaling behavior of the MBL transition. We present a suggestive construction that MBL is unstable for $d\ge 3$.

arXiv commentDiscussion on Hartree effects updated, 5 pages, 2 figures

References in corpus (57)

• Chaos and Quantum Thermalization
• 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
• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
• Interacting electrons in disordered wires: Anderson localization and low-temperature transport
• Phenomenology of fully many-body-localized systems
• A phenomenology of certain many-body-localized systems
• Local conservation laws and the structure of the many-body localized states
• On Many-Body Localization for Quantum Spin Chains
• Integrals of motion in the Many-Body localized phase
• Many-Body Localization in a Quasiperiodic System
• Quantum chaos challenges many-body localization
• Stability and instability towards delocalization in MBL systems
• Theory of the many-body localization transition in one dimensional systems
• Universal properties of many-body delocalization transitions
• Diagonalization and Many-Body Localization for a Disordered Quantum Spin Chain
• Avalanches and many-body resonances in many-body localized systems
• Two universality classes for the many-body localization transition
• Probing Slow Relaxation and Many-Body Localization in Two-Dimensional Quasi-Periodic Systems
• Thouless time analysis of Anderson and many-body localization transitions
• Review: Local Integrals of Motion in Many-Body Localized systems
• Dynamical obstruction to localization in a disordered spin chain
• Distinguishing localization from chaos: challenges in finite-size systems
• Ergodicity Breaking Transition in Finite Disordered Spin Chains
• Evidence for unbounded growth of the number entropy in many-body localized phases
• Many-body delocalization as a quantum avalanche
• Spectral features of a many-body localized system weakly coupled to a heat bath
• Can we study the many-body localisation transition?
• Analytically solvable renormalization group for the many-body localization transition
• Kosterlitz-Thouless scaling at many-body localization phase transitions
• Scaling Theory of Entanglement at the Many-Body Localization Transition
• A constructive theory of the numerically accessible many-body localized to thermal crossover
• Interaction instability of localization in quasiperiodic systems
• Many-body localization phase transition: A simplified strong-randomness approximate renormalization group
• Universal properties of many-body localization transitions in quasiperiodic systems
• Universality in the onset of quantum chaos in many-body systems
• Renormalization-group study of the many-body localization transition in one dimension
• Many-body delocalization dynamics in long Aubry-André quasiperiodic chains
• Instability of many-body localized systems as a phase transition in a nonstandard thermodynamic limit
• Many-body localization near the critical point
• Transport properties across the many-body localization transition in quasiperiodic and random systems
• On the stability of many-body localization in $d>1$
• Mixed spectra and partially extended states in a two-dimensional quasiperiodic model
• Chain breaking and Kosterlitz-Thouless scaling at the many-body localization transition in the random field Heisenberg spin chain
• A mean-field theory of nearly many-body localized metals
• Local resonances and parametric level dynamics in the many-body localised phase
• Universality and Quantum Criticality in Quasiperiodic Spin Chains
• Resonance-induced growth of number entropy in strongly disordered systems
• Finite-Size scaling analysis of many-body localization transition in quasi-periodic spin chains
• A self-consistent Hartree-Fock approach to Many-Body Localization
• Local integrals of motion and the quasiperiodic many-body localization transition
• Many-body localization in large systems: Matrix-product-state approach
• Dynamics of Many-Body Delocalization in the Time-dependent Hartree-Fock Approximation
• Quantum criticality in the 2d quasiperiodic Potts model

Cited by in corpus (19)

• Many-Body Localization in the Age of Classical Computing
• Coexistence of localization and transport in many-body two-dimensional Aubry-André models
• Hubbard Models for Quasicrystalline Potentials
• Mean field theory of failed thermalizing avalanches
• Quantum criticality and Kibble-Zurek scaling in the Aubry-André-Stark model
• Hybrid scaling properties of localization transition in a non-Hermitian disorder Aubry-André model
• Many-body localization crossover is sharper in quasiperiodic spin chains
• Stability of quasicrystalline ultracold fermions to dipolar interactions
• Non-equilibrium dynamics of localization phase transition in the non-Hermitian Disorder-Aubry-André model
• Interacting quasiperiodic spin chains in the prethermal regime
• Topological Phases of Many-Body Localized Systems: Beyond Eigenstate Order
• Logarithmic light cone, slow entanglement growth, and quantum memory
• Slow melting of a disordered quantum crystal
• Slowest and Fastest Information Scrambling in the Strongly Disordered XXZ Model
• Critical properties in the non-Hermitian Aubry-Andre-Stark model
• Engineering many-body quantum Hamiltonians with non-ergodic properties using quantum Monte Carlo
• Long-range resonances in quasiperiodic many-body localization
• Emergence of quasiperiodic behavior in transport and hybridization properties of clean lattice systems
• On the origin of energy gaps in quasicrystalline potentials