Fractionalized Kitaev model in a low magnetic field along [1 1 1

Abstract

Kitaev model in the presence of the magnetic field along the [111]-direction hosts topological excitations; the field dependence of the Kitaev model is specifically revisited in terms of fractionalized excitations. The weak-field limit is examined in terms of fractionalized spinon excitations employing Hartree-Fock BdG mean-field theory on a fermionized Kitaev model. We show that the original model of spins on a honeycomb lattice can be mapped on to a model of BCS superconductor constituting different kinds of pairing with a local constraint embodied in the model. It is also shown that the ground state Kitaev model has pairing on certain bonds forming a topological quantum order such as dimer model of valence bond solid in the low-field side. This order vanishes with the increasing magnetic field and at a critical field pairing vanishes, hence driving the system to a gapped phase.