Lattice CPT symmetry upgrades the Onsager chiral symmetry anomaly from order two to infinite order, better matching the continuum chiral anomaly, with discussion of associated 2+1d SPT phases.
Tori, Klein Bottles, and Modulo 8 Parity/Time-reversal Anomalies of 2+1d Staggered Fermions
4 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We study the symmetries of lattice staggered fermions in 2+1d. Using the symmetries, we can place the system on any sheared torus or Klein bottle. These different backgrounds provide diagnostics of various 't Hooft anomalies associated with the crystalline symmetries. We then compare the lattice model to its continuum limit. The symmetries of the lattice system are mapped in a nontrivial way to the symmetries of the continuum theories. Using this map, we match the 't Hooft anomalies on the lattice and the continuum. Along the way, we develop a general formalism to study Hamiltonian lattice models on nontrivial, compact, flat spaces.
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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.
A bosonic lattice model realizes exact chiral symmetry and its anomaly in 3+1d, with the continuum limit a compact boson theory with axion-like coupling.
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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Lattice fermion formulation via Physics-Informed Neural Networks: Ginsparg-Wilson relation and Overlap fermions
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.
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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.