Revisiting Entanglement Entropy of Lattice Gauge Theories

TL;DR

This paper clarifies the ambiguity in entanglement entropy for gauge theories, demonstrating that in certain models it is well-defined and providing a physical interpretation of the ambiguity in true gauge theories, with generalizations to non-Abelian cases.

Contribution

It shows that the topological entanglement entropy in the Kitaev model is unambiguous and offers a physical interpretation of the ambiguity in true gauge theories, extending to non-Abelian cases.

Findings

Kitaev model's entanglement entropy is unambiguous.

Ambiguity arises from boundary degrees of freedom in gauge theories.

Physical interpretation links ambiguity to boundary degree counting.

Abstract

Casini et al raise the issue that the entanglement entropy in gauge theories is ambiguous because its definition depends on the choice of the boundary between two regions.; even a small change in the boundary could annihilate the otherwise finite topological entanglement entropy between two regions. In this article, we first show that the topological entanglement entropy in the Kitaev model which is not a true gauge theory, is free of ambiguity. Then, we give a physical interpretation, from the perspectives of what can be measured in an experiement, to the purported ambiguity of true gauge theories, where the topological entanglement arises as redundancy in counting the degrees of freedom along the boundary separating two regions. We generalize these discussions to non-Abelian gauge theories.