Parity Anomaly of Lattice Maxwell Fermions in Two Spatial Dimensions

TL;DR

This paper investigates the parity anomaly of lattice Maxwell fermions in two dimensions, revealing their unique quantized Hall conductance and spontaneous parity breaking, which challenge the traditional fermion doubling theorem.

Contribution

It introduces the concept of parity anomaly for lattice Maxwell fermions in 2D, showing they can exist singly and contribute quantized Hall conductance beyond the fermion doubling theorem.

Findings

Maxwell fermions contribute a quantized Hall conductance of e^2/h.

Spontaneous parity breaking occurs in the effective theory.

Existence of single Maxwell fermion in lattice models beyond fermion doubling.

Abstract

Unconventional lattice fermions with high degeneracies beyond Weyl and Dirac fermions have attracted intensive attention in recent years. In this paper, attention is drawn to the pseudospin-1 Maxwell fermions and the $(2+1)$ dimensional parity anomaly, which goes beyond the scope of "fermion doubling theorem". We have derived the Hall conductivity of a single Maxwell fermion, and showcased each Maxwell fermion contributes a quantized Hall conductance $e^{2}/h$. We observe that the parity is spontaneously broken in the effective theory of lattice Maxwell fermions interacting with an (auxiliary) $U(1)$ gauge field, leading to an effective anomaly-induced Chern-Simons theory. An interesting observation from the parity anomaly is that the lattice Maxwell fermions beyond the "fermion doubling theorem", so there exists single Maxwell fermion in a lattice model. In addition, our work indicates the quantum anomaly in odd-dimensional spinor space.