Non-Abelian symmetry can increase entanglement entropy

The pillars of quantum theory include entanglement and operators' failure to commute. The Page curve quan-tifies 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 thermodynamics. For example, noncommuting charges were shown to reduce entropy-production rates and may enhance finite-size deviations from eigenstate thermalization. Bridging quantum thermodynamics to many-body physics, we quantify the 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 the noncommuting-charge case has more entanglement. Hence charges' noncommutation can promote entanglement.

Automated summary

The pillars of quantum theory, entanglement and operators' noncommutation, have important implications in quantum thermodynamics and many-body physics. The Page curve quantifies the entanglement of a many-body system, and it is known that noncommuting charges can promote entanglement. This study bridges quantum thermodynamics to many-body physics by exploring the effects of charges' noncommutation on the Page curves, showing that the noncommuting-charge case has more entanglement.