How a small quantum bath can thermalize long localized chains

Abstract

We investigate the stability of the many-body localized (MBL) phase for a system in contact with a single ergodic grain, modelling a Griffiths region with low disorder. Our numerical analysis provides evidence that even a small ergodic grain consisting of only 3 qubits can delocalize a localized chain, as soon as the localization length exceeds a critical value separating localized and extended regimes of the whole system. We present a simple theory, consistent with the arguments in [Phys. Rev. B 95, 155129 (2017)], that assumes a system to be locally ergodic unless the local relaxation time, determined by Fermi's Golden Rule, is larger than the inverse level spacing. This theory predicts a critical value for the localization length that is perfectly consistent with our numerical calculations. We analyze in detail the behavior of local operators inside and outside the ergodic grain, and find excellent agreement of numerics and theory.

4 pages, 5 figures

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• Fock-space anatomy of eigenstates across the many-body localisation transition
• Bath-induced decay of Stark many-body localization
• Stability of mobility edges in disordered interacting systems
• Detecting ergodic bubbles at the crossover to many-body localization using neural networks
• Catching thermal avalanches in the disordered XXZ model
• Perturbative instability towards delocalization at phase transitions between MBL phases
• Pair localization in dipolar systems with tunable positional disorder
• Lifetimes of local excitations in disordered dipolar quantum systems
• Edge mode locality in perturbed symmetry protected topological order
• Localization-delocalization effects of a delocalizing dissipation on disordered XXZ spin chains
• Universality in Non-Equilibrium Quantum Systems