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This research demonstrates that quantum group symmetries can coexist with chaotic dynamics in non-unitary, PT-symmetric spin chains, challenging the traditional association between such symmetries and integrability. By analyzing eigenvalue statistics, the study reveals a distinct transition where eigenvalues become complex, offering new insights into strongly correlated quantum systems beyond standard unitary frameworks.

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Chaos in Systems with Quantum Group Symmetry

arXivSeptember 9, 20261 min read

arXiv:2510.23247v3 Announce Type: replace-cross Abstract: Quantum groups have a long and fruitful history of applications in integrable systems. Can quantum group symmetries exist in the absence of integrability? We provide an explicit example of a system with quantum group global symmetry which is chaotic. The example is a spin chain with next-to-nearest interaction term. We show the chaotic behavior of the system by studying the Eigenvalue statistics. The spin chain is non-unitary but PT-symmetric and, in addition to chaos, exhibits an interesting transition after which the eigenvalues become complex.

Abstract:Quantum groups have a long and fruitful history of applications in integrable systems. Can quantum group symmetries exist in the absence of integrability? We provide an explicit example of a system with quantum group global symmetry which is chaotic. The example is a spin chain with next-to-nearest interaction term. We show the chaotic behavior of the system by studying the Eigenvalue statistics. The spin chain is non-unitary but PT-symmetric and, in addition to chaos, exhibits an interesting transition after which the eigenvalues become complex.

High Energy Physics - Theory (hep-th); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); Quantum Physics (quant-ph)

arXiv:2510.23247 [hep-th]

(or arXiv:2510.23247v3 [hep-th] for this version)

Phys.Rev.B 114 (2026) 10, 105123

https://doi.org/10.1103/vsqk-kk11 DOI(s) linking to related resources

Full text under the publisher's open licence · 119 words

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