Condensed Matter Theory

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 Z2 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.

Abstract:

Recent experiments use Fabry-Perot (FP) interferometry to claim that the ν=5/2 quantum Hall state exhibits non-Abelian topological order. We note that the experiments appear inconsistent with a model neglecting bulk-edge Coulomb coupling and Majorana tunneling, so we reexamine the theory of FP devices. Even a moderate Coulomb coupling may strongly affect some fractional plateaus, but very weakly affect others, allowing us to model the data over a wide range of plateaus. While experiments are consistent with the ν=5/2 state harboring Moore-Read topological order, they may have measured Coulomb effects rather than an "even-odd effect" due to non-Abelian braiding.