Anomalous multifractality in quantum chains with strongly correlated disorder

TL;DR

This paper uncovers a unique multifractal regime in a one-dimensional quantum chain with strongly correlated disorder, characterized by unusual eigenstate structures and ballistic transport, differing from conventional multifractality.

Contribution

It introduces a novel anomalous multifractal regime in quantum chains with maximally correlated disorder, highlighting its distinct eigenstate structure and transport properties.

Findings

Multifractal regime emerges above a disorder threshold.

Eigenstates are distributed over continuous segments with non-trivial scaling.

Ballistic transport persists over a system-size-dependent timescale.

Abstract

We demonstrate numerically that a robust and unusual multifractal regime can emerge in a one-dimensional quantum chain with maximally correlated disorder, above a threshold disorder strength. This regime is preceded by a mixed and an extended regime at weaker disorder strengths, with the former hosting both extended and multifractal eigenstates. The multifractal states we find are markedly different from conventional multifractal states in their structure, as they reside approximately uniformly over a continuous segment of the chain, and the lengths of these segments scale non-trivially with system size. This anomalous nature also leaves imprints on dynamics. An initially localised wavepacket shows ballistic transport, in contrast to the slow, generally sub-diffusive, transport commonly associated with multifractality. However, the timescale over which this ballistic transport persists again scales non-trivially with the system size.