Dynamics of Fractionalization in Quantum Spin Liquids

TL;DR

This paper provides an exact theoretical analysis of the dynamical spin-response in the Kitaev honeycomb model, revealing signatures of spin-fractionalization into Majorana fermions and fluxes across different quantum spin-liquid phases.

Contribution

It offers the first exact results for the structure factor in both gapped and gapless, Abelian and non-Abelian QSL phases, including methodological advances.

Findings

Structure factor shows signatures of spin-fractionalization.

Sharp features in response from flux-only and fermion-flux states.

Distinct differences in structure factor between Abelian and non-Abelian phases.

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 ($\delta$-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.