The Z N times 3 symmetry protected boundary modes in two-dimensional Potts paramagnets
The paper constructs and analyzes one-dimensional boundary Hamiltonians for two-dimensional symmetry-protected topological phases with a Z×3N symmetry on a triangular lattice. It finds that all nontrivial boundary theories can be described by primary models augmented by local 'defect' degrees of freedom, offering a unified description. The structure of these Hamiltonians depends on the arithmetic properties of N and explicitly realizes the ’t Hooft anomaly.