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arXiv · 2209.14303

Non-Abelian symmetry can increase entanglement entropy

Shayan Majidy·Aleksander Lasek·David A. Huse·Nicole Yunger Halpern
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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.

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Shayan Majidy, Aleksander Lasek, David A. Huse, Nicole Yunger Halpern. 2022-09-28. Non-Abelian symmetry can increase entanglement entropy. https://doi.org/10.1103/physrevb.107.045102

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