Parity Anomaly of Lattice Maxwell Fermions in Two Spatial Dimensions
arXiv:1912.11771 · doi:10.1088/1361-648X/ab985a
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 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 . We observe that the parity is spontaneously broken in the effective theory of lattice Maxwell fermions interacting with an (auxiliary) 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.
arXiv comment8 pages,2 figures
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