On the Relevance of Disorder for Dirac Fermions with Imaginary Vector Potential

TL;DR

This paper explores how disorder in an imaginary vector potential influences Dirac fermions, revealing two universality classes with different disorder relevance, impacting theoretical understanding of disordered quantum systems.

Contribution

It introduces the concept of disorder in an imaginary vector potential for Dirac Hamiltonians and identifies two distinct universality classes based on disorder strength.

Findings

Two universality classes depending on gauge and impurity disorder strengths

Gauge field disorder can render all disorder effects irrelevant

Sign changes in beta functions due to imaginary vector potential

Abstract

We consider the effects of disorder in a Dirac-like Hamiltonian. In order to use conformal perturbation theory, we argue that one should consider disorder in an imaginary vector potential. This affects significantly the signs of the lowest order $\beta$eta functions. We present evidence for the existence of two distinct universality classes, depending on the relative strengths of the gauge field verses impurity disorder strengths. In one class all disorder is driven irrelevant by the gauge field disorder.