Perturbative study of the Kitaev model with spontaneous time-reversal symmetry breaking

TL;DR

This paper investigates the Kitaev model on a triangle-honeycomb lattice, using perturbative expansions to explore its chiral spin liquid phase, effective theories, and the emergence of non-Abelian anyons.

Contribution

It provides a detailed perturbative analysis of the Kitaev model on a novel lattice, revealing effective theories and the conditions for non-Abelian anyons.

Findings

Derived low-energy effective theories in different limits

Computed spin-spin correlations for vortex configurations

Identified conditions for non-Abelian anyons emergence

Abstract

We analyze the Kitaev model on the triangle-honeycomb lattice whose ground state has recently been shown to be a chiral spin liquid. We consider two perturbative expansions: the isolated-dimer limit containing Abelian anyons and the isolated-triangle limit. In the former case, we derive the low-energy effective theory and discuss the role played by multi-plaquette interactions. In this phase, we also compute the spin-spin correlation functions for any vortex configuration. In the isolated-triangle limit, we show that the effective theory is, at lowest nontrivial order, the Kitaev honeycomb model at the isotropic point. We also compute the next-order correction which opens a gap and yields non-Abelian anyons.