Perturbed Kitaev model: excitation spectrum and long-ranged spin correlations

TL;DR

This paper develops a method to analyze long-range spin correlations in the perturbed Kitaev honeycomb model, revealing how specific interactions and magnetic fields influence the excitation spectrum and correlation functions.

Contribution

It introduces a general approach for calculating infrared asymptotics of spin correlations in the Kitaev model with perturbations, including an explicit fermionic density calculation method.

Findings

Dzyaloshinskii-Moriya interaction induces power-law spin correlations.

External magnetic field opens a gap in the excitation spectrum proportional to D and h.

Derived dynamical spin structure factor for the perturbed model.

Abstract

We developed general approach to the calculation of power-law infrared asymptotics of spin-spin correlation functions in the Kitaev honeycomb model with different types of perturbations. We have shown that in order to find these correlation functions, one can perform averaging of some bilinear forms composed out of free Majorana fermions, and we presented the method for explicit calculation of these fermionic densities. We demonstrated how to derive an effective Hamiltonian for the Majorana fermions, including the effects of perturbations. For specific application of the general theory, we have studied the effect of the Dzyaloshinskii-Moriya anisotropic spin-spin interaction; we demonstrated that it leads, already in the second order over its relative magnitude $D/K$, to a power-law spin correlation functions, and calculated dynamical spin structure factor of the system. We have shown that an external magnetic field $h$ in presence of the DM interaction, opens a gap in the excitation spectrum of magnitude $\Delta \propto D h$.