Spin correlations and phase diagram of the perturbed Kitaev model

TL;DR

This paper classifies perturbations in the Kitaev model based on their impact on spin correlations, deriving conditions for long-range behavior, and studies the phase diagram including phase transitions and stability of spin-liquid phases.

Contribution

It provides a comprehensive classification of perturbations affecting spin correlations in the Kitaev model and analyzes the resulting phase diagram with phase transitions.

Findings

Perturbations can induce confinement-deconfinement transitions.

Long-range power-law spin correlations depend on specific perturbations.

The model exhibits topological quantum phase transitions between gapped and gapless spin liquids.

Abstract

We present a general classification of the perturbations to the Kitaev model on the basis of their effect on it's spin correlation functions. We derive a necessary and sufficient condition for the spin correlators to exhibit a long ranged power-law behavior in the presence of such perturbations. We substantiate our result by a study of the phase diagram of the Kitaev model augmented by a loop term and perturbed by an Ising term, within a RVB mean-field theory. We estimate the stability of the spin-liquid phase against such perturbations and show that this model exhibits both confinement-deconfinement transitions from spin liquid to antiferromagnetic/spin-chain/ferromagnetic phases as well as topological quantum phase transitions between gapped and gapless spin liquid phases.