Entanglement of a 3D generalization of the Kitaev model on the diamond lattice

TL;DR

This paper investigates the entanglement properties of a 3D generalization of the Kitaev model on a diamond lattice, revealing how topological entanglement entropy and spectrum distinguish phases and how vortex lines affect entanglement.

Contribution

It provides a systematic analysis of entanglement in a 3D Kitaev model using fermionic tools, highlighting the role of the $Z_2$ gauge field and Majorana fermions in topological phases.

Findings

Topological entanglement entropy originates solely from the $Z_2$ gauge field.

Entanglement spectrum of Majorana fermions distinguishes topological phases.

Vortex lines modify the entanglement contribution of Majorana modes.

Abstract

We study the entanglement properties of a three dimensional generalization of the Kitaev honeycomb model proposed by Ryu [Phys. Rev. B 79, 075124, (2009)]. The entanglement entropy in this model separates into a contribution from a $Z_2$ gauge field and that of a system of hopping Majorana fermions, similar to what occurs in the Kitaev model. This separation enables the systematic study of the entanglement of this 3D interacting bosonic model by using the tools of non-interacting fermions. In this way, we find that the topological entanglement entropy comes exclusively from the $Z_2$ gauge field, and that it is the same for all of the phases of the system. There are differences, however, in the entanglement spectrum of the Majorana fermions that distinguish between the topologically distinct phases of the model. We further point out that the effect of introducing vortex lines in the $Z_2$ gauge field will only change the entanglement contribution of the Majorana fermions. We evaluate this contribution to the entanglement which arises due to gapless Majorana modes that are trapped by the vortex lines.