Dynamical structure factor in the non-Abelian phase of the Kitaev honeycomb model in the presence of quenched disorder

TL;DR

This paper analytically investigates the dynamical structure factor of the non-Abelian phase in the Kitaev honeycomb model, considering quenched disorder, revealing signatures of spin-liquid behavior relevant for experimental detection.

Contribution

It provides an analytical calculation of the dynamical spin structure factor in the non-Abelian phase with quenched disorder, including Majorana zero modes and vortex effects.

Findings

Identifies a low-energy peak as a signature of the spin-liquid phase.

Maps the model to a chiral p-wave superconductor to analyze Majorana modes.

Calculates energy splitting and wave functions of Majorana zero modes.

Abstract

Kitaev's model of spins interacting on a honeycomb lattice describes a quantum spin-liquid, where an emergent static $\mathbb{Z}_2$ gauge field is coupled to Majorana fermions. In the presence of an external magnetic field and for a range of interaction strengths, the system behaves as a gapped, non-Abelian quantum spin-liquid. In this phase, the vortex excitations of the emergent $\mathbb{Z}_2$ gauge field have Majorana zero modes bound to them. Motivated by recent experimental progress in measuring and characterizing real materials that could exhibit spin-liquid behavior, we analytically calculate the dynamical spin structure factor in the non-Abelian phase of the Kitaev's honeycomb model. In particular, we treat the case of quenched disorder in the vortex configurations. Our calculations reveal a peak in the low-energy dynamical structure factor that is a signature of the spin-liquid behavior. We map the effective Hamiltonian to that of a chiral p-wave superconductor by using the Jordan-Wigner transformation. Subsequently, we analytically calculate the wave functions of the Majorana zero modes, the energy splitting for finite separation of the vortices and finally, the dynamical structure factor in presence of quenched disorder.