Entanglement entropy in lattice theories with Abelian gauge groups

TL;DR

This paper investigates the conditions under which the Hilbert space of lattice Abelian gauge theories can be decomposed into tensor products, focusing on entanglement entropy and the impact of boundary conditions and topological degrees of freedom.

Contribution

It clarifies when the Hilbert space of lattice Abelian theories admits a geometric tensor product structure, especially highlighting the role of boundary conditions and topological sectors.

Findings

Hilbert space is geometrically separable except in pure gauge lattices with periodic boundaries.

Topological degrees of freedom affect the tensor product structure.

Conditions for tensor product decomposition are explicitly discussed.

Abstract

We revisit the issue of the geometrical separability of the Hilbert space of physical states on lattice Abelian theories in the context of entanglement entropy. We discuss the conditions under which vectors in the Hilbert space, as well as the gauge invariant algebra, admit a tensor product decomposition with a geometrical interpretation. With the exception of pure gauge lattices with periodic boundary conditions which contain topological degrees of freedom, we show that the Hilbert space is geometrically separable.