Entanglement Entropy in Pure $Z_2$ Gauge Lattices

TL;DR

This paper demonstrates that the physical Hilbert space of pure $Z_2$ gauge lattices in 1+1 and 2+1 dimensions is geometrically separable when using plaquettes as degrees of freedom, and introduces a model linking physical and link-based entanglement entropy.

Contribution

It introduces a lattice model that equates physical entanglement entropy with that calculated from link degrees of freedom, independent of gauge fixing.

Findings

Physical states' Hilbert space is geometrically separable.

Entanglement entropy is unaffected by gauge fixing.

Non-physical gauge states reveal boundary constraints.

Abstract

We show that the Hilbert space of physical states on a pure $Z_2$ gauge lattice in $1 + 1$ and $2 + 1$ dimensions is geometrically separable if the fundamental physical degrees of freedom are taken to be the plaquettes. This results in a physical entanglement entropy that is not affected by gauge fixing. We introduce a lattice model that is physically equivalent to the original and whose entanglement entropy, calculated using link degrees of freedom, is the same as the entanglement entropy calculated using physical states. We also show that, for non-physical gauge link states, entanglement entropy quantifies constraints between gauge choices in plaquettes adjacent to the boundary.