Kitaev model on Hurwitz hyperbolic tilings: A non-Abelian gapped chiral spin liquid

TL;DR

This paper investigates the Kitaev model on a hyperbolic tiling, revealing that odd loops induce chiral spin liquids with non-Abelian anyons, advancing understanding of topological quantum states.

Contribution

It introduces the Kitaev model on Hurwitz hyperbolic tilings, demonstrating spontaneous time-reversal symmetry breaking and non-Abelian gapped chiral spin liquids.

Findings

Presence of odd-length loops causes time-reversal symmetry breaking.

Ground states are gapped chiral spin liquids with non-Abelian excitations.

Elementary excitations are non-Abelian Ising anyons.

Abstract

We study the Kitaev model on the trivalent heptagonal Hurwitz hyperbolic tiling. The presence of odd-length loops in the tiling is responsible for a spontaneous time-reversal symmetry breaking. Interestingly, at the isotropic point, the two degenerate ground states (Kramers pair) are shown to be gapped chiral spin liquids and the elementary excitations are non-Abelian Ising anyons.