Non-Abelian symmetry can increase entanglement entropy

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 (A...

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Bibliographic Details
Published in:arXiv.org 2023-01
Main Authors: Majidy, Shayan, Lasek, Aleksander, Huse, David A, Nicole Yunger Halpern
Format: Article
Language:English
Subjects:
Eigenvectors
Entropy
Quantum entanglement
Quantum theory
Symmetry
Thermalization (energy absorption)
Thermodynamics
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2209.14303