Emergent Fermions and Anyons in the Kitaev Model

TL;DR

This paper investigates the low-energy excitations in the Kitaev honeycomb model, revealing emergent anyons and fermions, and introduces a perturbative approach that avoids traditional fermionization techniques.

Contribution

It provides an analytical perturbative method to analyze the Kitaev model's excitations without relying on Majorana or Jordan-Wigner fermionization.

Findings

Effective low-energy Hamiltonian is an extended toric code with interacting anyons.

High-energy excitations are emergent free fermions composed of hardcore bosons.

Excitation spectrum maps onto a single particle hopping in a magnetic field.

Abstract

We study the gapped phase of the Kitaev model on the honeycomb lattice using perturbative continuous unitary transformations. The effective low-energy Hamiltonian is found to be an extended toric code with interacting anyons. High-energy excitations are emerging free fermions which are composed of hardcore bosons with an attached string of spin operators. The excitation spectrum is mapped onto that of a single particle hopping on a square lattice in a magnetic field. We also illustrate how to compute correlation functions in this framework. The present approach yields analytical perturbative results in the thermodynamical limit without using the Majorana or the Jordan-Wigner fermionization initially proposed to solve this problem.