Generalized Entanglement, Charges and Intertwiners

TL;DR

This paper develops a generalized entanglement entropy framework for quantum systems with internal symmetries, incorporating charge contributions and bi-local intertwiners, applicable to both lattice models and quantum field theory.

Contribution

It introduces a new entanglement measure that accounts for charge sectors and bi-local intertwiners, bridging lattice models and QFT with a unified approach.

Findings

New entanglement measure includes charge-neutral and intertwiners contributions.

Application of Tomita-Takesaki theory to distinguish QFT and lattice models.

Extension of QFT algebra enables factorization of charged modes.

Abstract

The entanglement theory in quantum systems with internal symmetries is rich due to the spontaneous creation of entangled pairs of charge/anti-charge particles at the entangling surface. We call these pair creation operators the bi-local intertwiners because of the role they play in the representation theory of the symmetry group. We define a generalized measure of entanglement entropy as a measure of information erased under restriction to a subspace of observables. We argue that the correct entanglement measure in the presence of charges is the sum of two terms; one measuring the entanglement of charge-neutral operators, and the other measuring the contribution of the bi-local intertwiners. Our expression is unambiguously defined in lattice models as well in quantum field theory (QFT). We use the Tomita-Takesaki modular theory to highlight the differences between QFT and lattice models, and discuss an extension of the algebra of QFT that leads to a factorization of the charged modes.