Localization crossover and subdiffusive transport in a classical facilitated network model of a disordered, interacting quantum spin chain

TL;DR

This paper introduces a classical facilitated hopping model to study many-body localization phenomena, revealing a transition from diffusive to subdiffusive transport influenced by thermal bubbles, providing insights into quantum MBL systems coupled to environments.

Contribution

It presents a classical model that captures the crossover and transition behaviors of many-body localization in quantum systems with bath coupling, highlighting the role of thermal bubbles.

Findings

Identification of a crossover between ergodic and localized phases.

Observation of a transition from diffusive to subdiffusive transport.

Demonstration of classical long memory times analogous to quantum MBL.

Abstract

We consider the random-field Heisenberg model, a paradigmatic model for many-body localization (MBL), and add a Markovian dephasing bath coupled to the Anderson orbitals of the model's non-interacting limit. We map this system to a classical facilitated hopping model that is computationally tractable for large system sizes, and investigate its dynamics. The classical model exhibits a robust crossover between an ergodic (thermal) phase and a frozen (localized) phase. The frozen phase is destabilized by thermal subregions (bubbles), which thermalize surrounding sites by providing a fluctuating interaction energy and so enable off-resonance particle transport. Investigating steady state transport, we observe that the interplay between thermal and frozen bubbles leads to a clear transition between diffusive and subdiffusive regimes. This phenomenology both describes the MBL system coupled to a bath, and provides a classical analogue for the many-body localization transition in the corresponding quantum model, in that the classical model displays long local memory times. It also highlights the importance of the details of the bath coupling in studies of MBL systems coupled to thermal environments.