Chiral Gapless Spin Liquid in Hyperbolic Space

TL;DR

This paper explores the Kitaev model on a hyperbolic lattice, revealing a gapless chiral $3$ spin liquid state with spontaneous time reversal symmetry breaking and potential non-Abelian quasiparticles.

Contribution

It introduces a generalization of the Kitaev model to hyperbolic space and uncovers a novel gapless chiral spin liquid with unique symmetry properties.

Findings

Identification of a gapless chiral $3$ spin liquid in hyperbolic space

Spontaneous time reversal symmetry breaking observed

Potential for non-Abelian quasiparticles due to non-commutative translation group

Abstract

We analyze the Kitaev model on the $\{9,3\}$ hyperbolic lattice. The $\{9,3\}$ is formed by a regular tricoordinated 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 Euclidean regular honeycomb tiling. Upon investigation of the bulk spectrum for large finite size droplets, we identify a gapless chiral $\mathbb{Z}_2$ 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.