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

## TL;DR

This paper introduces an exact fermionization method to analyze a honeycomb lattice Kitaev model with Wen-Toric-code interactions, revealing rich phase diagrams and anyon excitations.

## Contribution

A new fermionization technique for 2D systems is developed, enabling exact analysis of the Kitaev model with additional Wen-Toric-code interactions and exploration of anyon excitations.

## Key findings

- Exact ground state phase diagram obtained.
- Anyons appear in each phase of the model.
- Generalized 2D Jordan-Wigner transformation derived.

## Abstract

The honeycomb lattice Kitaev model H_{K} with two kinds of Wen-Toric-code four-body interactions H_{WT} 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 H_{K}+H_{WT} is symmetric in four-dimensional space of coupling constants, and the anyon type excitations appear in each phase.