Chiral Anomaly in Interacting Condensed Matter Systems

TL;DR

This paper explores how interactions influence the chiral anomaly in Weyl semimetals, revealing modifications to chiral charge dynamics and non-linear responses due to quantum interactions and electromagnetic fields.

Contribution

It demonstrates that interactions modify the chiral charge continuity equation and affect the non-linear electromagnetic response in Weyl semimetals, combining Fujikawa's method with Luttinger liquid theory.

Findings

Interaction-dependent density response to magnetic field changes

Modification of chiral charge conservation by interactions

Altered non-equilibrium anomalous Hall response

Abstract

The chiral anomaly is a fundamental quantum mechanical phenomenon which is of great importance to both particle physics and condensed matter physics alike. In the context of QED it manifests as the breaking of chiral symmetry in the presence of electromagnetic fields. It is also known that anomalous chiral symmetry breaking can occur through interactions alone, as is the case for interacting one dimensional systems. In this paper we investigate the interplay between these two modes of anomalous chiral symmetry breaking in the context of interacting Weyl semimetals. Using Fujikawa's path integral method we show that the chiral charge continuity equation is modified by the presence of interactions which can be viewed as including the effect of the electric and magnetic fields generated by the interacting quantum matter. This can be understood further using dimensional reduction and a Luttinger liquid description of the lowest Landau level. These effects manifest themselves in the non-linear response of the system. In particular we find an interaction dependent density response due to a change in the magnetic field as well as a contribution to the non-equilibrium and inhomogeneous anomalous Hall response while preserving its equilibrium value.