Disordered Weyl semimetal as an array of coupled Hubbard chains

TL;DR

This paper maps a disordered magnetic Weyl semimetal onto a 2D array of coupled Hubbard chains, revealing it becomes a diffusive metal with finite density of states even at weak disorder, and discusses localization absence.

Contribution

It introduces a novel mapping of disordered Weyl semimetals to coupled Hubbard chains, extending previous 2D to 1D mappings, and provides insights into disorder effects and localization.

Findings

Weyl semimetal maps to coupled Hubbard chains with disorder related to Hubbard U.

Disordered Weyl semimetal becomes a diffusive metal with nonzero density of states at weak disorder.

Absence of localization explained via the coupled chain mapping.

Abstract

We demonstrate that a disordered magnetic Weyl semimetal may be mapped onto a two-dimensional array of coupled replicated Hubbard chains, where the Hubbard $U$ is directly related to the variance of the disorder potential. This is a three-dimensional generalization of a similar mapping of the two-dimensional quantum Hall plateau transition to a one-dimensional Hubbard chain. We demonstrate that this mapping leads to the conclusion that the Weyl semimetal becomes a diffusive metal with a nonzero density of states at arbitrarily weak disorder, in agreement with recent work. We also discuss the absence of localization in strongly disordered Weyl semimetals from the viewpoint of this mapping.