Subdiffusion in a 1D Anderson insulator with random dephasing: Finite-size scaling, Griffiths effects, and possible implications for many-body localization

TL;DR

This paper investigates the transition from diffusive to subdiffusive transport in a disordered 1D quantum system with dephasing, revealing Griffiths effects and finite-size scaling, with implications for many-body localization.

Contribution

It introduces a toy model mimicking many-body localization phenomena, providing exact solutions and analyzing critical properties related to Griffiths effects in disordered quantum systems.

Findings

Transition from diffusive to subdiffusive transport observed

Finite-size scaling explained by interplay of disorder, dephasing, and rare regions

Heavy-tailed resistance distributions may be absent due to logarithmic growth of insulating regions

Abstract

We study transport in a one-dimensional boundary-driven Anderson insulator (the XX spin chain with onsite disorder) with randomly positioned onsite dephasing, observing a transition from diffusive to subdiffusive spin transport below a critical density of sites with dephasing. This model is intended to mimic the passage of an excitation through (many-body) insulating regions or ergodic bubbles, therefore providing a toy model for the diffusion-subdiffusion transition observed in the disordered Heisenberg model [1]. We also present the exact solution of a semiclassical model of conductors and insulators introduced in Ref. 2, which exhibits both diffusive and subdiffusive phases, and qualitatively reproduces the results of the quantum system. The critical properties of both models, when passing from diffusion to subdiffusion, are interpreted in terms of "Griffiths effects". We show that the finite-size scaling comes from the interplay of three characteristic lengths: one associated with disorder (the localization length), one with dephasing, and the third with the percolation problem defining large, rare, insulating regions. We conjecture that the latter, which grows logarithmically with system size, may potentially be responsible for the fact that heavy-tailed resistance distributions typical of Griffiths effects have not been observed in subdiffusive interacting systems.