Non-Abelian symmetry can increase entanglement entropy

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

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


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.

Original languageEnglish (US)
Article number045102
JournalPhysical Review B
Issue number4
StatePublished - Jan 15 2023

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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