Mean field theory of failed thermalizing avalanches

Abstract

We show that localization in quasiperiodically modulated, two-dimensional systems is stable to the presence of a finite density of ergodic grains. This contrasts with the case of randomly modulated systems, where such grains seed thermalizing avalanches. These results are obtained within a quantitatively accurate, self-consistent entanglement mean field theory which analytically describes two level systems connected to a central ergodic grain. The theory predicts the distribution of entanglement entropies of each two level system across eigenstates, and the late time values of dynamical observables. In addition to recovering the known phenomenology of avalanches, the theory reproduces exact diagonalization data, and predicts the spatial profile of the thermalized region when the avalanche fails.

13 pages, 5 figures

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• Scale-invariant critical dynamics at eigenstate transitions
• Restoring ergodicity in a strongly disordered interacting chain
• Statistics of systemwide correlations in the random-field XXZ chain: Importance of rare events in the many-body localized phase
• Beyond Fermi's golden rule with the statistical Jacobi approximation
• Renormalization view on resonance proliferation between many-body localized phases
• Finite steady-state current defies non-Hermitian many-body localization
• Logarithmic light cone, slow entanglement growth, and quantum memory
• Slow melting of a disordered quantum crystal
• Scaling theory of fading ergodicity
• Sub-ballistic operator growth in spin chains with heavy-tailed random fields
• Unconventional Thermalization of a Localized Chain Interacting with an Ergodic Bath
• Quantum simulation of the microscopic to macroscopic crossover using superconducting quantum impurities
• On the origin of energy gaps in quasicrystalline potentials