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The "non-regularizability" of gapless free fermion Hamiltonian protected by on-site symmetries

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.

preprint2020arXivOpen access
Yen-Ta HuangLokman TsuiDung-Hai Lee
cond-mat.str-el
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Yen-Ta HuangLokman TsuiDung-Hai Lee

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