Phenomenology of anomalous transport in disordered one-dimensional systems

TL;DR

This paper investigates the distribution of resistance in disordered one-dimensional spin chains exhibiting anomalous subdiffusive transport, challenging the Griffiths picture by finding no evidence of fat-tailed distributions.

Contribution

It provides new insights into the resistance distribution in many-particle disordered systems, questioning the role of rare regions in slow transport phenomena.

Findings

No evidence of fat-tailed resistance distributions.

Data compatible with faster-than-power-law decay.

Gaussian distribution suggested for fractional resistance power.

Abstract

We study anomalous transport arising in disordered one-dimensional spin chains, specifically focusing on the subdiffusive transport typically found in a phase preceding the many-body localization transition. Different types of transport can be distinguished by the scaling of the average resistance with the system's length. We address the following question: what is the distribution of resistance over different disorder realizations, and how does it differ between transport types? In particular, an often evoked so-called Griffiths picture, that aims to explain slow transport as being due to rare regions of high disorder, would predict that the diverging resistivity is due to fat power-law tails in the resistance distribution. Studying many-particle systems with and without interactions we do not find any clear signs of fat tails. The data is compatible with distributions that decay faster than any power law required by the fat tails scenario. Among the distributions compatible with the data, a simple additivity argument suggests a Gaussian distribution for a fractional power of the resistance.