Formulas for Partial Entanglement Entropy

TL;DR

This paper establishes a unique formula for partial entanglement entropy in Poincaré invariant theories, validating the PEE proposal by demonstrating it meets all physical requirements and is uniquely determined.

Contribution

The paper introduces a new physical requirement for PEE and proves the PEE proposal is uniquely determined and justified in Poincaré invariant theories.

Findings

PEE can be uniquely determined by physical requirements

The PEE proposal satisfies all physical criteria

First proof of the uniqueness of PEE in this context

Abstract

The partial entanglement entropy (PEE) $s_{\mathcal{A}}(\mathcal{A}_i)$ characterizes how much the subset $\mathcal{A}_i$ of $\mathcal{A}$ contribute to the entanglement entropy $S_{\mathcal{A}}$. We find one additional physical requirement for $s_{\mathcal{A}}(\mathcal{A}_i)$, which is the invariance under a permutation. The partial entanglement entropy proposal satisfies all the physical requirements. We show that for Poincar\'e invariant theories the physical requirements are enough to uniquely determine the PEE (or the entanglement contour) to satisfy a general formula. This is the first time we find the PEE can be uniquely determined. Since the solution of the requirements is unique and the \textit{PEE proposal} is a solution, the \textit{PEE proposal} is justified for Poincar\'e invariant theories.