The Kekul\'e-Kitaev model: linear and non-linear responses and magnetic field effects

TL;DR

This paper investigates the Kekule9-Kitaev model's linear and nonlinear magnetic responses, revealing unique behaviors under magnetic fields and connecting its ground state to excited states of the Kitaev model.

Contribution

It provides the first detailed analysis of the Kekule9-Kitaev model's dynamical responses and magnetic field effects, highlighting its distinct non-Abelian phase behavior.

Findings

Linear and nonlinear responses are qualitatively similar to the Kitaev model.

The Kekule9-Kitaev model lacks a non-Abelian phase under a uniform magnetic field.

Signals from two non-adjacent fluxes dominate in the nonlinear response within the non-Abelian phase.

Abstract

The Kekul\'e-Kitaev model, an extension of the Kitaev model, exhibits quantum spin liquid (QSL) properties, which has an exact solution through Kitaev parton construction. In this study, we calculate the dynamical spin structure factor as a linear response and the third-order magnetic susceptibility as a nonlinear response using two-dimensional coherent spectroscopy for Kekul\'e-Kitaev model. Our results reveal that the few-matter fermion excitations approximation provides reliable results for both linear and nonlinear responses. Notably, while the Kekul\'e-Kitaev model shows linear and nonlinear responses qualitatively similar to the Kitaev model, it displays distinct behavior under a weak uniform/staggered magnetic field. Specifically, the Kekul\'e-Kitaev model does not present a non-Abelian phase under a uniform magnetic field, while such phase appears in the presence of a staggered magnetic field. Interestingly, within the non-Abelian phase, signals originating from two non-adjacent fluxes in the nonlinear response are stronger than signals from other flux excitations. Furthermore, We demonstrate that the ground state of the Kekul\'e-Kitaev model at isotropic coupling is mapped, through unitary spin rotations, to an excited state of the Kitaev model with a uniform flux configuration.