Multifractality and its role in anomalous transport in the disordered XXZ spin-chain

TL;DR

This paper investigates the multifractal nature of eigenstates in the disordered XXZ spin-chain and its connection to anomalous transport, using advanced numerical methods to analyze systems up to 24 spins.

Contribution

It provides the first large-scale numerical evidence linking multifractality of many-body eigenstates to subdiffusive transport near the MBL transition.

Findings

A large fraction of the delocalized phase approaches ergodicity in the thermodynamic limit.

A region near the MBL transition appears multifractal in the thermodynamic limit.

Implications for the mechanism of subdiffusive transport are discussed.

Abstract

The disordered XXZ model is a prototype model of the many-body localization transition (MBL). Despite numerous studies of this model, the available numerical evidence of multifractality of its eigenstates is not very conclusive due severe finite size effects. Moreover it is not clear if similarly to the case of single-particle physics, multifractal properties of the many-body eigenstates are related to anomalous transport, which is observed in this model. In this work, using a state-of-the-art, massively parallel, numerically exact method, we study systems of up to 24 spins and show that a large fraction of the delocalized phase flows towards ergodicity in the thermodynamic limit, while a region immediately preceding the MBL transition appears to be multifractal in this limit. We discuss the implication of our finding on the mechanism of subdiffusive transport.