The "non-regularizability" of gapless free fermion Hamiltonian protected by on-site symmetries
arXiv:1907.02522 · doi:10.1016/j.nuclphysb.2020.115005
Abstract
The non-regularizability of free fermion field theories, which is the root of various quantum anomalies, plays a central role in particle physics and modern condensed matter physics. In this paper, we generalize the Nielsen-Ninomiya theorem to all minimal nodal free fermion field theories protected by the time reversal, charge conservation, and charge conjugation symmetries. We prove that these massless field theories cannot be regularized on a lattice.
29 pages, 4 figures