Hyperbolic Spin Liquids

TL;DR

This paper extends Kitaev's spin-1/2 honeycomb model to hyperbolic lattices, revealing novel quantum spin liquid phases and topological states in negatively curved space.

Contribution

It provides the first exact solution of a Kitaev model on hyperbolic lattices, uncovering new gapped and gapless spin liquid phases with exotic anyonic excitations.

Findings

Identified a gapped $ ext{Z}_2$ spin liquid with Abelian anyons

Discovered a gapped chiral spin liquid with non-Abelian anyons and edge states

Found a Majorana metal with non-Abelian Bloch states and finite low-energy density of states

Abstract

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. We elucidate the ground-state phase diagram on the $\{8,3\}$ lattice and find a gapped $\mathbb{Z}_2$ spin liquid with Abelian anyons, a gapped chiral spin liquid with non-Abelian anyons and chiral edge states, and a Majorana metal whose finite low-energy density of states is dominated by non-Abelian Bloch states.