Chiral Gapless Spin Liquid in Hyperbolic Space

Recently, interacting quantum models in hyperbolic space became a subject of interest in theoretical condensed matter physics. In this talk, we analyze the Kitaev model on the {9, 3} hyperbolic lattice. This lattice is formed by a regular 3-coordinated tiling of nonagons, where the 3-color coding of bonds according to the inequivalent Kitaev Ising spin couplings yields the natural generalization of the original Kitaev model for the Euclidean honeycomb tiling. Upon investigation of the bulk spectrum, we identify a gapless chiral spin liquid state featuring spontaneous time-reversal symmetry breaking. Due to its non-commutative translation group structure, such type of hyperbolic spin liquid is conjectured to feature chiral quasiparticles with a potentially non-Abelian Bloch profile.