PINNs optimize Dirac operators to satisfy the Ginsparg-Wilson relation, reproducing overlap fermions and autonomously recovering both the standard and a Fujikawa-type generalized GW relation via polynomial ansatz search.
Chi- ral Anomaly of Kogut-Susskind Fermion in (3+1)- dimensional Hamiltonian formalism
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A kink in a one-link mass term for 3+1D staggered fermions creates a 2+1D domain wall with two-flavor massless Dirac fermions protected by SU(2) and parity, realizing the parity anomaly from the UV lattice Hamiltonian.
A noncompact Lie group symmetry generated by U(1) fermion number and Majorana translations enforces Fermi surfaces that generically have at least two noncontractible components in d-dimensional Bravais lattices.
Minimal-doubling lattice fermion Hamiltonians yield single-Weyl phases when supplemented by a species-splitting mass term, but one-parameter symmetry-preserving deformations introduce additional Weyl nodes above a critical value.
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Symmetry-Enforced Fermi Surfaces
A noncompact Lie group symmetry generated by U(1) fermion number and Majorana translations enforces Fermi surfaces that generically have at least two noncontractible components in d-dimensional Bravais lattices.
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Minimal-doubling and single-Weyl Hamiltonians
Minimal-doubling lattice fermion Hamiltonians yield single-Weyl phases when supplemented by a species-splitting mass term, but one-parameter symmetry-preserving deformations introduce additional Weyl nodes above a critical value.