Universal observable as a signal of chiral anomaly in lattice Weyl fermions

TL;DR

This paper demonstrates that a rotationally invariant observable derived from magnetoconductivities acts as a universal signal of the chiral anomaly in lattice Weyl fermions, remaining robust across various conditions and symmetries.

Contribution

It introduces a universal observable $kappa$ as a robust signature of the chiral anomaly in lattice Weyl systems, valid beyond moderate magnetic fields and independent of system anisotropies.

Findings

$kappa$ exhibits a universal $B^2$ dependence.

$kappa$ scales with $| ext{cos} heta|$, where $ heta$ is the angle between $ extbf{E}$ and $ extbf{B}.

The universality of $kappa$ persists despite anisotropies and system parameter variations.

Abstract

The Adler-Bell-Jackiw chiral anomaly is shown to retain its Lorentz-invariant form, $\partial_\mu J^\mu_5 \propto \mathbf{E} \cdot \mathbf{B}$, in lattice Weyl systems beyond moderate magnetic fields, where neither Lorentz nor rotational symmetry is present. We show that the longitudinal and Hall magnetoconductivities factorize into a product of a universal part, governed by the chiral anomaly, and a non-universal part that depends on the density of states at the Fermi level. A rotationally invariant observable $\varkappa = \sigma (c_V/T)^2$ is introduced as a robust signature of the anomaly, where $\sigma$ denotes the Euclidean norm of the longitudinal and Hall conductivities and $c_V$ is the specific heat density. This quantity follows a universal $B^2$ dependence and scales as $|\cos\Theta|$, with $\Theta$ being the angle between $\mathbf{E}$ and $\mathbf{B}$. Through analytical derivation and full numerical simulation, we establish that $\varkappa$ remains universal independent of system parameters and of the orientation of the magnetic or electric field for fixed $\Theta$. The emergent SO(3) symmetry in $\varkappa$ persists despite the absence of isotropy in both the microscopic model and the low-energy effective theory.