SU(2) Slave Fermion Solution of the Kitaev Honeycomb Lattice Model

TL;DR

This paper uses the SU(2) slave fermion approach to analyze the Kitaev honeycomb model, revealing its phases as p-wave superconductors and explaining phase transitions, including the non-Abelian phase under magnetic field.

Contribution

It provides a novel fermionic formalism to understand the phase diagram and excitations of the Kitaev honeycomb model, connecting it to superconducting phases.

Findings

Toric Code and gapless phases correspond to p-wave superconductors.

Non-Abelian phase is a p+ip superconductor under magnetic field.

Phase transitions are described within the slave fermion framework.

Abstract

We apply the SU(2) slave fermion formalism to the Kitaev honeycomb lattice model. We show that both the Toric Code phase (the A phase) and the gapless phase of this model (the B phase) can be identified with p-wave superconducting phases of the slave fermions, with nodal lines which, respectively, do not or do intersect the Fermi surface. The non-Abelian Ising anyon phase is a $p+ip$ superconducting phase which occurs when the B phase is subjected to a gap-opening magnetic field. We also discuss the transitions between these phases in this language.