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

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 ∆ ∝ Dh.

Impact of off-diagonal exchange interactions on the Kitaev spin-liquid state of α−RuCl3

“…The energy gap of itinerant Majorana fermions linear in a magnetic field was predicted before from a general symmetrical argument, 5 or by considering a model with the Dzyaloshinskii-Moriya interaction. 34 In contrast to these previous studies, however, our result is based on the microscopic analysis of the realistic model for candidate materials of Kitaev magnets.…”

Novel Chiral Quantum Spin Liquids in Kitaev Magnets

“…Recent numerical studies [11][12][13][14][15][16][17][18][19][20][21][22][28][29][30][31][32][33] suggest the existence of a gapless intermediate phase in a somewhat similar parameter range. In spite of the different features found (gapless vs gapped), our gap closing around B c can be associated with the large enhancement of low energy excitations developing near the PL phase.…”

“…On the other hand, the effect of Heisenberg and symmetric spin exchange terms needs to be considered [16,17] in order to accurately describe the magnetically ordered phases [18] observed in Na 2 IrO 3 and α-RuCl 3 . Finally, the next-nearest-neighbor Dzyaloshinskii-Moriya (DM) has been invoked as being relevant for the description of real materials [19] but its effect on the Kitaev model remains little explored so far [20].…”