Superselection Rules, Bosonization Duality in 1+1 Dimensions and Momentum-Space Entanglement

TL;DR

This paper explores how superselection rules influence momentum-space entanglement in 1+1 dimensional QFTs, especially under bosonization duality, revealing how different partitions relate and proposing conditions for generalization.

Contribution

It introduces a framework connecting superselection sectors with momentum-space entanglement and analyzes their behavior under bosonization duality in 1+1 dimensions.

Findings

Superselection sectors lead to different momentum mode notions.

Bosonization duality maps tensor product partitions of momentum space.

Explicit examples demonstrate the duality's effect on entanglement partitions.

Abstract

We investigate the effects of the presence of conserved charges on the momentum-space entanglement of Quantum Field Theories (QFTs). We show that if a given model has superselection sectors, then it allows for different notions of momentum modes, each associated with a complete set of commuting observables. Applying this idea to investigate the entanglement of momentum degrees of freedom on both sides of the abelian Bosonization duality, we find that different tensor product partitions are mapped into each other and give explicit examples to sustain our findings. The conditions on which our conclusions may be generalized to other duality transformations, which require the introduction of a notion stricter than the most general possible, are laid and directions for further work are given.