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

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.

12 pages

References in corpus (13)

• Generalized Global Symmetries
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Entanglement in an expanding spacetime
• Entanglement in fermionic systems
• Dynamical structure factor at small q for the XXZ spin-1/2 chain
• Lecture Notes on Generalized Symmetries and Applications
• Bose-Fermi duality and entanglement entropies
• Entanglement Entropy in (3+1)-d Free $U(1)$ Gauge Theory
• Momentum Space Entanglement from the Wilsonian Effective Action
• Categorical-Symmetry Resolved Entanglement in CFT
• Bosonization duality in 2+1 dimensions and critical current correlation functions in Chern-Simons $U(1)\times U(1)$ Abelian Higgs model
• Wilsonian Renormalization as a Quantum Channel and the Separability of Fixed Points
• Exact Renormalization of Wave Functionals yields Continuous MERA