Non-Abelian symmetry can increase entanglement entropy
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.
Cite
@article{arxiv.2209.14303,
title = {Non-Abelian symmetry can increase entanglement entropy},
author = {Shayan Majidy and Aleksander Lasek and David A. Huse and Nicole Yunger Halpern},
journal= {arXiv preprint arXiv:2209.14303},
year = {2023}
}
Comments
4.5 pages (2 figures) + appendices (12 pages)