Generalized Kitaev Models and Slave Genons

TL;DR

This paper introduces a broad class of integrable lattice models extending the Kitaev honeycomb model, utilizing a 'slave-genon' approach to embed spin systems into non-Abelian defect frameworks, revealing potential non-Abelian topological phases.

Contribution

It develops a generalized framework for Kitaev-like models using genons, enabling exact reformulation and analysis of non-Abelian topological phases in lattice systems.

Findings

Models exhibit infinite conserved quantities and topological degeneracy.

The 'slave-genon' approach generalizes Majorana fermions to non-Abelian defects.

A specific $Z_3$ model may realize non-Abelian topological order with chiral edge states.

Abstract

We present a wide class of partially integrable lattice models with two-spin interactions, which generalize the Kitaev honeycomb model. These models have an infinite number of conserved quantities associated with each plaquette of the lattice, conserved large loop operators on the torus, and protected topological degeneracy. We introduce a `slave-genon' approach, which generalizes the Majorana fermion approach in the Kitaev honeycomb model. The Hilbert space of our spin model can be embedded into an enlarged Hilbert space of non-Abelian twist defects, referred to as genons. In the enlarged Hilbert space, the spin model is exactly reformulated as a model of non-Abelian genons coupled to a discrete gauge field. We discuss in detail a particular $Z_3$ generalization, and show that in a certain limit the model is analytically tractable and may produce a non-Abelian topological phase with chiral parafermion edge states.