Boundary topological entanglement entropy in two and three dimensions

TL;DR

This paper derives explicit formulas for boundary topological entanglement entropy in 2D and 3D loop gas models, linking it to fusion category data and generalized S-matrices, advancing understanding of quantum correlations in topological phases.

Contribution

It provides closed-form expressions for boundary topological entanglement entropy in higher dimensions based on fusion categories and introduces conjectures about generalized S-matrices.

Findings

Explicit formulas for 2D and 3D topological entanglement entropy

Connection between entropy and fusion category data

Proofs for categories up to rank 5

Abstract

The topological entanglement entropy is used to measure long-range quantum correlations in the ground state of topological phases. Here we obtain closed form expressions for topological entropy of (2+1)- and (3+1)-dimensional loop gas models, both in the bulk and at their boundaries, in terms of the data of their input fusion categories and algebra objects. Central to the formulation of our results are generalized $\mathcal{S}$-matrices. We conjecture a general property of these $\mathcal{S}$-matrices, with proofs provided in many special cases. This includes constructive proofs for categories up to rank 5.