Non-Abelian symmetry can increase entanglement entropy

TL;DR

This paper demonstrates that non-Abelian symmetries, characterized by noncommuting charges, can enhance entanglement entropy in quantum many-body systems, contrasting with Abelian symmetries where charges commute.

Contribution

It provides the first quantitative analysis of how non-Abelian symmetries influence entanglement, showing that noncommuting charges can increase entanglement entropy.

Findings

Non-Abelian charges lead to higher entanglement entropy.

Models with noncommuting charges exhibit more entanglement than those with commuting charges.

Analytical and numerical results confirm the entanglement increase due to non-Abelian symmetries.

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 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.