Parity anomaly of lattice Maxwell fermions in two spatial dimensions

Unconventional lattice fermions with high degeneracies that are not Weyl or Dirac fermions have attracted increased attention in recent years. In this paper, we consider pseudospin-1 Maxwell fermions and the (2 + 1)-dimensional parity anomaly, which are not constrained by the fermion doubling theorem. We derive the Hall conductivity of a single Maxwell fermion and explain how each Maxwell fermion has a quantized Hall conductance ofe²/h. 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 about the parity anomaly is that the lattice Maxwell fermions are not constrained by the fermion doubling theorem, so a single Maxwell fermion can exist in a lattice. In addition, our work considers the quantum anomaly in odd-dimensional spinor space.