Chiral magnetic conductivity in an interacting lattice model of parity-breaking Weyl semimetal

TL;DR

This study investigates how interactions influence the chiral magnetic conductivity in a lattice model of Weyl semimetals, finding that interactions mainly renormalize the chiral chemical potential and have limited impact on the CME response.

Contribution

It provides a mean-field analysis of the CME in an interacting lattice Weyl semimetal, including nontrivial corrections from ladder diagrams, highlighting the limited practical relevance of interaction-induced corrections.

Findings

Interactions mainly renormalize the chiral chemical potential.

Nontrivial corrections are negligible unless the CME is suppressed by a large energy gap.

On-site repulsive interactions do not significantly alter the CME in typical conditions.

Abstract

We report on the mean-field study of the Chiral Magnetic Effect (CME) in static magnetic fields within a simple model of a parity-breaking Weyl semimetal given by the lattice Wilson-Dirac Hamiltonian with constant chiral chemical potential. We consider both the mean-field renormalization of the model parameters and nontrivial corrections to the CME originating from re-summed ladder diagrams with arbitrary number of loops. We find that on-site repulsive interactions affect the chiral magnetic conductivity almost exclusively through the enhancement of the renormalized chiral chemical potential. Our results suggest that nontrivial corrections to the chiral magnetic conductivity due to inter-fermion interactions are not relevant in practice, since they only become important when the CME response is strongly suppressed by the large gap in the energy spectrum.