Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations

TL;DR

This paper provides exact analytical results for the Kitaev honeycomb model, revealing the structure of its ground states, non-local correlators, topological order, and anyonic excitations using a Jordan-Wigner transformation.

Contribution

It introduces a direct solution method for the Kitaev model, expressing ground states and correlators in terms of spins and fermions, and elucidates topological and anyonic properties.

Findings

Explicit spin representation of fermionic ground states

Symmetry-determined string and brane correlators

Topological order encoded in states, independent of spectrum

Abstract

In this work, we illustrate how a Jordan-Wigner transformation combined with symmetry considerations enables a direct solution of Kitaev's model on the honeycomb lattice. We (i) express the p-wave type fermionic ground states of this system in terms of the original spins, (ii) adduce that symmetry alone dictates the existence of string and planar brane type correlators and their composites, (iii) compute the value of such non-local correlators by employing the Jordan-Wigner transformation, (iv) affirm that the spectrum is inconsequential to the existence of topological quantum order and that such information is encoded in the states themselves, and (v) express the anyonic character of the excitations in this system and the local symmetries that it harbors in terms of fermions.