Decomposition of entanglement entropy in lattice gauge theory

TL;DR

This paper analyzes how entanglement entropy in lattice gauge theories can be decomposed into boundary and nonlocal contributions, highlighting the dominant role of edge states in various examples.

Contribution

It introduces a decomposition of entanglement entropy into boundary and nonlocal terms, emphasizing the significance of edge states in lattice gauge theories.

Findings

Edge states dominate entanglement entropy in studied examples.

Entropy decomposes into classical, non-Abelian, and nonlocal terms.

Results apply to ground states in strong coupling regimes.

Abstract

We consider entanglement entropy between regions of space in lattice gauge theory. The Hilbert space corresponding to a region of space includes edge states that transform nontrivially under gauge transformations. By decomposing the edge states in irreducible representations of the gauge group, the entropy of an arbitrary state is expressed as the sum of three positive terms: a term associated with the classical Shannon entropy of the distribution of boundary representations, a term that appears only for non-Abelian gauge theories and depends on the dimension of the boundary representations, and a term representing nonlocal correlations. The first two terms are the entropy of the edge states, and depend only on observables measurable at the boundary. These results are applied to several examples of lattice gauge theory states, including the ground state in the strong coupling expansion of Kogut and Susskind. In all these examples we find that the entropy of the edge states is the dominant contribution to the entanglement entropy.