A fermionic Villain lattice Hamiltonian exactly realizes the chiral U(1) L x U(1) R symmetry and anomalies of a massless Dirac fermion, enabling exact studies of symmetric mass generation and chiral lattice gauge theories.
Generalized BKT Transitions and Persistent Order on the Lattice
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abstract
The BKT transition in low-dimensional systems with a $U(1)$ global symmetry separates a gapless conformal phase from a trivially gapped, disordered phase, and is driven by vortex proliferation. Recent developments in modified Villain discretizations provide a class of lattice models which have a $\mathbb{Z}_W$ global symmetry that counts vortices mod W, mixed 't Hooft anomalies, and persistent order even at finite lattice spacing. While there is no fully-disordered phase (except in the original BKT limit $W=1$) there is still a phase boundary which separates gapped ordered phases from gapless phases. I'll describe a numerical Monte Carlo exploration of these phenomena.
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Fermionic Villain model with exact lattice chiral symmetries
A fermionic Villain lattice Hamiltonian exactly realizes the chiral U(1) L x U(1) R symmetry and anomalies of a massless Dirac fermion, enabling exact studies of symmetric mass generation and chiral lattice gauge theories.