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 $d\ge 3$.

Discussion on Hartree effects updated, 5 pages, 2 figures

References in corpus (12)

• Many body localization and thermalization in quantum statistical mechanics
• Localization of interacting fermions at high temperature
• Phenomenology of fully many-body-localized systems
• Integrals of motion in the Many-Body localized phase
• Many-Body Localization in a Quasiperiodic System
• Ergodicity Breaking Transition in Finite Disordered Spin Chains
• Can we study the many-body localisation transition?
• Renormalization-group study of the many-body localization transition in one dimension
• 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
• A mean-field theory of nearly many-body localized metals

Cited by in corpus (18)

• 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
• Slow melting of a disordered quantum crystal
• Interacting quasiperiodic spin chains in the prethermal regime
• Logarithmic light cone, slow entanglement growth, and quantum memory
• Topological Phases of Many-Body Localized Systems: Beyond Eigenstate Order
• Slowest and Fastest Information Scrambling in the Strongly Disordered XXZ Model
• Critical properties in the non-Hermitian Aubry-Andre-Stark model
• Long-range resonances in quasiperiodic many-body localization
• On the origin of energy gaps in quasicrystalline potentials
• Emergence of quasiperiodic behavior in transport and hybridization properties of clean lattice systems