Hyperbolic lattices present a unique opportunity to venture beyond the conventional paradigm of crystalline many-body physics and explore correlated phenomena in negatively curved space. As a theoretical benchmark for such investigations, we extend Kitaev’s spin-1/2 honeycomb model to hyperbolic lattices and exploit their non-Euclidean space-group symmetries to solve the model exactly. In this Wolfram Mathematica notebook, we first show how to construct Kitaev models on hyperbolic lattices. Subsequently, we demonstrate how to use hyperbolic band theory to obtain the ground-state phase diagram on one of them and study the phases therein. In particular, we study the exotic compressible spin liquid with low-energy density of states dominated by non-Abelian Bloch states of Majorana fermions appearing for isotropic couplings which develops into a gapped chiral spin liquid under a time-reversal-breaking perturbation.
