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

Abstract

The Adler-Bell-Jackiw chiral anomaly is shown to retain its Lorentz-invariant form, ${\partial }_{\hat{I}}¼J^{\hat{I}}{¼}_5\propto \mathbf{E}\cdot \mathbf{B}$, 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 $\varkappa =\ddot{I}ƒ(c_V/T{)}^2$ is introduced as a robust signature of the anomaly, where $\ddot{I}ƒ$ 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 $|\cos \hat{I}˜|$, with $\hat{I}˜$ 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 $\hat{I}˜$. The emergent SO(3) symmetry in $\varkappa$ persists despite the absence of isotropy in both the microscopic model and the low-energy effective theory.

6 pages, 3 figures