Avalanche induced co-existing localised and thermal regions in disordered chains

Abstract

We investigate the stability of an Anderson localised chain to the inclusion of a single finite interacting thermal seed. This system models the effects of rare low-disorder regions on many-body localised chains. Above a threshold value of the mean localisation length, the seed causes runaway thermalisation in which a finite fraction of the orbitals are absorbed into a thermal bubble. This 'partially avalanched' regime provides a simple example of a delocalised, non-ergodic dynamical phase. We derive the hierarchy of length scales necessary for typical samples to exhibit the avalanche stability, and show that the required seed size diverges at the avalanche threshold. We introduce a new dimensionless statistic that measures the effective size of the thermal bubble, and use it to numerically confirm the predictions of avalanche theory in the Anderson chain at infinite temperature.

Emergent ergodicity at the transition between many-body localized phases

“…Moreover, we demonstrate that this emergent ergodicity is intimately tied to the presence of a phase transition; a disorder-less, symmetry-breaking field suppresses the intervening ergodic phase. In addition to numerics, we analyze two instabilities which could induce thermalization near the putative transition: (i) the proliferation of two-body resonances [2,31,32] and (ii) the run-away of avalanches [33,34]. We find that the latter is marginal.…”

“…Alternatively, one might consider the susceptibility to 'avalanches' due to rare thermal bubbles induced by the interactions [33,67,68]. For a system with a distribution of localization lengths, it has recently been shown that the average localization length controls this instability [34]: for ξ > 2/ log 2, thermal bubbles avalanche. However, this is within a model where the orbitals have a single localization center.…”

Persistent dark states in anisotropic central spin models

“…Refs. [68,69]. Chaos manifests in the exponential scaling of the Frobenius norm of the AGP with system size, which can be interpreted as an exponential sensitivity of the eigenstates to perturbations of the Hamiltonian.…”