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

Abstract

We investigate the nonlinear response of the Kitaev honeycomb lattice model in a weak magnetic field using the theory of two-dimensional coherent spectroscopy. We observe that at the isotropic point in the non-Abelian 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, 2-non-adjacent, 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.

Two-dimensional coherent spectrum of high-spin models via a quantum computing approach

“…By measuring the material's time-dependent response to one, two or more THz pulses, which corresponds to one-dimensional coherent spectrum (1DCS), two-dimensional coherent spectrum (2DCS), and generally multi-dimensional coherent spectrum (MDCS), the spin dynamics, energy levels, as well as interactions between the spins can be probed. 2DCS has also been discussed theoretically as a powerful probe of observing fractionalization, decoherence, and wavefunction properties in quantum spin liquids [27][28][29][30][31], low-dimensional magnets [32][33][34][35][36][37], and random magnets [38]. It has been experimentally demonstrated that THz pulses enable the detection [39,40] and coherent control [41] of collective excitations in the spin degrees of freedom, with their quanta referred to as magnons [42].…”