Entropic Topological Invariants in Three Dimensions

TL;DR

This paper investigates the entanglement entropy in three-dimensional topological models, revealing richer topological invariants than in 2D, including a new invariant related to anyon braiding.

Contribution

It introduces a new topological invariant affecting entanglement entropy in 3D models, expanding understanding beyond 2D topological entanglement entropy.

Findings

Entanglement entropy in 3D models shows richer topological features.

A new invariant increases entropy in models with non-trivially braiding anyons.

3D topological entanglement entropy partially captures topological invariants.

Abstract

We evaluate the entanglement entropy of exactly solvable Hamiltonians corresponding to general families of three-dimensional topological models. We show that the modification to the entropic area law due to three-dimensional topological properties is richer than the two-dimensional case. In addition to the reduction of the entropy caused by non-zero vacuum expectation value of contractible loop operators a new topological invariant appears that increases the entropy if the model consists of non-trivially braiding anyons. As a result the three-dimensional topological entanglement entropy provides only partial information about the two entropic topological invariants.