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This research demonstrates that entanglement asymmetry can scale extensively in quantum systems with Hilbert-space fragmentation, challenging previous bounds observed in conventional symmetric states. By generalizing the measure using commutant algebra formalism, the study provides a critical tool for distinguishing between classical and quantum fragmentation regimes. These findings offer new insights into the universal behavior of U(1) charges within complex, disconnected quantum sectors.

Sources coveringQuantum Zeitgeist, arXiv, terrytao.wordpress.com

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Quantum asymmetry can grow faster in broken systems

Quantum ZeitgeistOctober 13, 20266 min read

Entanglement asymmetry, a measure of symmetry breaking, is typically limited—but in systems with Hilbert-space fragmentation, this asymmetry can scale extensively.

Researchers have generalized a measure of symmetry breaking, entanglement asymmetry, to account for quantum systems fracturing into exponentially many disconnected sectors. Lorenzo Gotta of the University of Geneva, Filiberto Ares of SISSA and INFN and Sara Murciano of Université Paris-Saclay demonstrate that while asymmetry typically has an upper bound, it can scale extensively in these fragmented systems. This distinction allows researchers to differentiate between “classical” and “quantum” fragmentation, a key insight into the behavior of complex quantum states. The work qualitatively reproduces recent findings on asymmetry dynamics in random quantum circuits, suggesting a universal behavior for these U(1) charges in local ergodic systems. Entanglement asymmetry, a quantitative measure of symmetry breaking in quantum states, typically…

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