Topological entanglement entropy of three-dimensional Kitaev model

TL;DR

This paper calculates the topological entanglement entropy for a 3D Kitaev model, revealing it is not solely determined by the total quantum dimension, unlike in many other models.

Contribution

It provides the first calculation of TEE for a 3D Kitaev model and shows its deviation from the expected relation to quantum dimension.

Findings

TEE is not directly determined by the total quantum dimension in this 3D model.

Provides TEE for a 3D toric-code-type Hamiltonian as an effective low-energy theory.

Highlights differences between 2D and 3D topological entanglement properties.

Abstract

We calculate the topological entanglement entropy (TEE) for a three-dimensional hyperhoneycomb lattice generalization of Kitaev's honeycomb lattice spin model. We find that for this model TEE is not directly determined by the total quantum dimension of the system. This is in contrast to general two dimensional systems and many three dimensional models, where TEE is related to the total quantum dimension. Our calculation also provides TEE for a three-dimensional toric-code-type Hamiltonian that emerges as the effective low-energy theory for the Kitaev model in a particular limit.