Nonlinear response of the Kitaev honeycomb lattice model in a weak magnetic field

We investigate the nonlinear response of the Kitaev honeycomb lattice model in a weak magnetic field using the theory of two-dimensional (2D) coherent spectroscopy. We observe that at the isotropic point in the nonAbelian phase of this model, the nonlinear spectrum in the 2D frequency domain consists of sharp signals that originate from the flux excitations and Majorana bound states. Signatures of different flux excitations can be clearly observed in this spectrum, such that one can observe evidences of flux states with 4-adjacent, 2nonadjacent, and 4-far-separated fluxes, which are not visible in linear response spectroscopy such as neutron scattering experiments. Moreover, in the Abelian phase we perceive that the spectrum in the frequency domain is composed of streak signals. These signals, as in the nonlinear response of the pure Kitaev model, represent a distinct signature of itinerant Majorana fermions. However, deep in the Abelian phase whenever a Kitaev exchange coupling is much stronger than the others, the streak signals are weakened and only single sharp spots are seen in the response, which resembles the dispersionless response of the conventional toric code.

Automated summary

We study the nonlinear response of the Kitaev honeycomb lattice model in a weak magnetic field using 2D coherent spectroscopy. In the nonAbelian phase, the nonlinear spectrum in the frequency domain consists of sharp signals originating from flux excitations and Majorana bound states. Different flux excitations, including 4-adjacent, 2-nonadjacent, and 4-far-separated fluxes, are clearly observed in this spectrum. In the Abelian phase, the spectrum is composed of streak signals representing the presence of itinerant Majorana fermions. However, in the deep Abelian phase with a dominant Kitaev exchange coupling, the streak signals weaken and single sharp spots resembling the dispersionless response of the conventional toric code are observed.