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.
Lattice Fermions Based on Higher-Dimensional Hyperdiamond Lattices
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abstract
In this paper we generalize to higher dimensions several types of fermion actions on the hyperdiamond lattice including a two-parameter class of minimal-doubling fermions "Creutz fermion" and a simple fermion with sufficient discrete symmetry "BBTW fermion". Then it is shown that they possess some properties in common with the four-dimensional case: BBTW fermions in higher even dimensions inevitably yield unphysical degrees of freedom. Creutz fermions are defined on the distorted lattices, and they lose the high discrete symmetry of the original lattices. We also find properties specific to the higher-dimensional cases. The parameter range for Creutz action to yield minimal-doubling and physical fermions becomes narrower with the dimension getting higher, thus it becomes more and more difficult to realize minimal-doubling. In addition, we generalize the subspecies of Creutz and BBTW actions including a new class of minimal-doubling actions "Appended Creutz action".
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UNVERDICTED 2representative citing papers
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.