Topological excitations in three dimensional Kitaev model

TL;DR

This paper investigates the nature of topological excitations in a three-dimensional Kitaev model, revealing fermionic loop excitations with nontrivial braiding properties, advancing understanding of 3D topological quantum systems.

Contribution

It introduces a low energy effective Hamiltonian for the 3D Kitaev model and characterizes the loop-like fermionic excitations and their braiding statistics.

Findings

Elementary excitations are fermionic loops.

Excitations obey nontrivial braiding rules with phase π.

The gapped phase is described by a Hamiltonian on the diamond lattice.

Abstract

We study the excitations in a three dimensional version of Kitaev's spin-1/2 model on the honeycomb lattice introduced by the present authors recently. The gapped phase of the system is analyzed using a low energy effective Hamiltonian which is defined on the diamond lattice and consists of plaquette operators. The excitations of the effective Hamiltonian form loops in an embedded lattice. The elementary excitations, which are the shortest loops, are fermions. Moreover, the excitations obey nontrivial braiding rules: when a fermion winds through a loop, the wave function acquires a phase $\pi$.