Dynamics of fractionalization in quantum spin liquids

Abstract

We present the theory of dynamical spin response for the Kitaev honeycomb model, obtaining exact results for the structure factor (SF) in gapped and gapless, Abelian and non-Abelian quantum spin-liquid (QSL) phases. We also describe the advances in methodology necessary to compute these results. The structure factor shows signatures of spin fractionalization into emergent quasiparticles: Majorana fermions and fluxes of Z 2 gauge field. In addition to a broad continuum from spin fractionalization, we find sharp ( δ -function) features in the response. These arise in two distinct ways: from excited states containing only (static) fluxes and no (mobile) fermions, and from excited states in which fermions are bound to fluxes. The SF is markedly different in Abelian and non-Abelian QSLs, and bound fermion-flux composites appear only in the non-Abelian phase.