Honeycomb lattice Kitaev model with Wen–Toric-code interactions, and anyon excitations

Abstract

The honeycomb lattice Kitaev model HK with two kinds of Wen–Toric-code four-body interactions HWT is investigated exactly using a new fermionization method, and the ground state phase diagram is obtained. Six kinds of three-body interactions are also considered. A Hamiltonian equivalent to the honeycomb lattice Kitaev model is also introduced. The fermionization method is generalized to two-dimensional systems, and the two-dimensional Jordan–Wigner transformation is obtained as a special case of this formula. The model HK+HWT is symmetric in four-dimensional space of coupling constants, and the anyon type excitations appear in each phase.