2025/11/01 by Xianghong Kong, Kong, Xianghong, Xingsi Liu +10
Physics and Astronomy · Mathematics · #Topological Materials and Phenomena #Algebraic structures and combinatorial models #Physics of Superconductivity and Magnetism
paper · pdf · doi:10.48550/arxiv.2511.00380
A systematic framework for realizing ℤ2 gauge extensions of hyperbolic lattices within the nearest-neighbor tight-binding formalism is developed. Using the triangle group Δ(2,8,8) as an example, we classify all inequivalent projective symmetry groups by computing the second cohomology group H2(Δ(2,8,8),ℤ2). Each class corresponds to a distinct flux configuration and can be constructed by tight-binding models to verify the symmetry relations of the extended group. The translation subgroups of the ℤ2 extended lattices are associated with high genus surfaces, which follows the Riemann-Hurwitz formula. By applying the Abelian hyperbolic band theory, we find the all-flat dispersions along specific directions in momentum space and van Hove singularities correlated with discrete eigenenergies. Our results establish a general route to investigate gauge-extended hyperbolic lattices and provide a foundation for further studying symmetry fractionalization and spin liquid phases in non-Euclidean geometries.