Physics-Informed Neural Networks construct lattice Dirac operators satisfying the Ginsparg-Wilson relation, reproducing overlap fermions to high accuracy and discovering a Fujikawa-type generalized relation via algebraic search.
Index Theorem and Overlap Formalism with Naive and Minimally Doubled Fermions
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abstract
We present a theoretical foundation for the Index theorem in naive and minimally doubled lattice fermions by studying the spectral flow of a Hermitean version of Dirac operators. We utilize the point splitting method to implement flavored mass terms, which play an important role in constructing proper Hermitean operators. We show the spectral flow correctly detects the index of the would-be zero modes which is determined by gauge field topology. Using the flavored mass terms, we present new types of overlap fermions from the naive fermion kernels, with a number of flavors that depends on the choice of the mass terms. We succeed to obtain a single-flavor naive overlap fermion which maintains hypercubic symmetry.
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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.
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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Lattice fermion formulation via Physics-Informed Neural Networks: Ginsparg-Wilson relation and Overlap fermions
Physics-Informed Neural Networks construct lattice Dirac operators satisfying the Ginsparg-Wilson relation, reproducing overlap fermions to high accuracy and discovering a Fujikawa-type generalized relation via algebraic search.
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Taste-splitting mass and edge modes in $3+1$ D staggered fermions
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.
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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.