Exact results for spin dynamics and fractionization in the Kitaev Model

TL;DR

This paper provides exact analytical results for spin dynamics in the Kitaev Model, revealing a short-range spin liquid behavior and a unique fractionalization process involving Majorana fermions and fluxes, with implications for topological quantum computation.

Contribution

It presents the first exact analytical results for dynamical spin correlation functions in a non-trivial quantum spin model, highlighting novel fractionalization phenomena.

Findings

Dynamical two-spin correlations are zero beyond nearest neighbors.

Existence of a gapless but short-range spin liquid.

Spin-flip quanta fractionalize into massive fluxes and Majorana fermions.

Abstract

We present certain exact analytical results for dynamical spin correlation functions in the Kitaev Model. It is the first result of its kind in non-trivial quantum spin models. The result is also novel: in spite of presence of gapless propagating Majorana fermion excitations, dynamical two spin correlation functions are identically zero beyond nearest neighbor separation, showing existence of a gapless but short range spin liquid. An unusual, \emph{all energy scale fractionization}of a spin -flip quanta, into two infinitely massive $\pi$-fluxes and a dynamical Majorana fermion, is shown to occur. As the Kitaev Model exemplifies topological quantum computation, our result presents new insights into qubit dynamics and generation of topological excitations.