This paper fermionizes the modified Villain model, producing an exactly solvable lattice Hamiltonian whose low-energy sector is a Dirac fermion with exact non-onsite U(1)_V and U(1)_A symmetries.
Lieb-Schultz-Mattis, Luttinger, and ’t Hooft - anomaly matching in lattice systems.SciPost Physics, 15(2):051, August 2023
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1+1d Lattice Dirac Fermions from Non-Onsite Vector and Axial Symmetries
This paper fermionizes the modified Villain model, producing an exactly solvable lattice Hamiltonian whose low-energy sector is a Dirac fermion with exact non-onsite U(1)_V and U(1)_A symmetries.