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

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.