Destruction of Localization by Thermal Inclusions: Anomalous Transport and Griffiths Effects in the Anderson and Andr\'e-Aubry-Harper Models

TL;DR

This paper compares toy models for anomalous transport and Griffiths effects near many-body localization transitions, showing how thermal inclusions influence transport properties in random and quasiperiodic systems.

Contribution

It introduces and compares two models for thermal inclusions in localized systems and extends them to quasiperiodic potentials, revealing Griffiths-like phenomena.

Findings

Both models exhibit Griffiths-like phenomenology.

GOE bath is less effective in thermalization.

Quasiperiodic systems show subdiffusive transport.

Abstract

We discuss and compare two recently proposed toy models for anomalous transport and Griffiths effects in random systems near the Many-Body Localization transitions: the random dephasing model, which adds thermal inclusions in an Anderson Insulator as local Markovian dephasing channels that heat up the system, and the random Gaussian Orthogonal Ensemble (GOE) approach which models them in terms of ensembles of random regular graphs. For these two settings we discuss and compare transport and dissipative properties and their statistics. We show that both types of dissipation lead to similar Griffiths-like phenomenology, with the GOE bath being less effective in thermalising the system due to its finite bandwidth. We then extend these models to the case of a quasi-periodic potential as described by the Andr\'e-Aubry-Harper model coupled to random thermal inclusions, that we show to display, for large strength of the quasiperiodic potential, a similar phenomenology to the one of the purely random case. In particular, we show the emergence of subdiffusive transport and broad statistics of the local density of states, suggestive of Griffiths like effects arising from the interplay between quasiperiodic localization and random coupling to the baths.