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.
On the suitability of the Brillouin action as a kernel to the overlap procedure
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abstract
We investigate the Brillouin action in terms of its suitability as a kernel to the overlap procedure, with a view on both heavy and light quark physics. We use the diagonal elements of the Kenney-Laub family of iterations for the sparse matrix sign function, since they grow monotonically and facilitate cascaded preconditioning strategies with different rational approximations to the sign function. We find that the overlap action with the Brillouin kernel is significantly better localized than the version with the Wilson kernel.
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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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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.