Modified Villain lattice realizations of flat-gauged interfaces and T-duality defects in the 2D compact boson are constructed at arbitrary radii, yielding non-compact edge modes with continuous spectrum and infinite quantum dimension.
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Lattice T- duality from non-invertible symmetries in quantum spin chains
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Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.
Introduces the twisted Villain model to realize exact T-duality on the lattice for fibred manifolds, recovering bundle-flux exchange and defining topological defects via half-gauging.
Defect 't Hooft anomalies trap charges at symmetry-line junctions and thereby drive categorical scattering into twist operators.
Z_k symmetries from Pythagorean triples in two free Weyl fermions yield non-invertible defects that generate all U(1)^2-preserving boundaries for two Dirac fermions.
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 noncompact Lie group symmetry generated by U(1) fermion number and Majorana translations enforces Fermi surfaces that generically have at least two noncontractible components in d-dimensional Bravais lattices.
Entangling power in Heisenberg spin chains shows a monotonic decrease with growing symmetry in small models, sharp dips at SU(2) and free-fermion points in finite chains, and vanishes at SU(2) points but maximizes at the free-fermion point in the thermodynamic limit for the S-matrix.
Deconfined criticality in a 1D lattice model is shown to be an intrinsically gapless topological state whose mixed anomaly enforces robust edge modes without gapped counterparts.
Staggered fermions in 2+1d show modulo 8 parity/time-reversal anomalies that match between lattice and continuum when placed on tori and Klein bottles via a nontrivial symmetry map.
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A Twist on Scattering from Defect Anomalies
Defect 't Hooft anomalies trap charges at symmetry-line junctions and thereby drive categorical scattering into twist operators.