Abstract: The pillars of quantum theory include entanglement and operators' failure to commute. The Page curve quantifies the bipartite entanglement of a many-body system in a random pure state. This entanglement is known to decrease if one constrains extensive observables that commute with each other (Abelian ``charges''). Non-Abelian charges, which fail to commute with each other, are of current interest in quantum information and thermodynamics. For example, noncommuting charges were shown to reduce entropy-production rates and conflict with the eigenstate thermalization hypothesis. We quantify effects of charges' noncommutation—of a symmetry's non-Abelian nature—on Page curves. First, we construct two models that are closely analogous but differ in whether their charges commute. We show analytically and numerically that noncommuting charges raise the Page curve, promoting entanglement on average. This result raises questions about whether charges’ noncommutation can hinder or enhance thermalization and information storage.
Ref: Shayan Majidy, Aleks Lasek, David Huse, and Nicole Yunger Halpern "Non-Abelian symmetry can increase entanglement entropy." Physical Review B 107.4 (2023): 045102.