Topological phase transition in the field induced Kitaev model on the Kagome lattice

We investigate the low-energy spectral properties of the Kitaev model on the Kagome lattice, which is a quantum spin model for the aim of fault-tolerant quantum computation, in the presence of a uniform magnetic field in the x- and z-directions. We explore the low-energy physics of the Kitaev model in the x- and z-magnetic fields, separately and establish a quasi-particle picture for anyonic excitations. Our study is based on the high-order series expansion of the low- and high field limits of the problem by means of perturbative continuous unitary transformations. We further show that the Kitaev model in the x-field is mapped to the Ising transverse field (ITF) model on the triangular lattice while, the system is mapped to another ITF model on the honeycomb lattice in the presence of the z-magnetic field. Additionally, we investigate the phase transitions of the model for the two cases and find that the topological phase of the Kitaev model breaks down to the polarized phase in either x- or z-directions by a second-order quantum phase transition in the 3D Ising universality class. We further detect dispersive bound states in high-field limits of the model for both cases of the magnetic field. The overall results further indicate that the Kitaev model on the Kagome lattice has the different stability as the toric code on the square lattice, while perturbed by magnetic fields.