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Chaos in Systems with Quantum Group Symmetry
Victor Gorbenko, Aleksandr Zhabin·October 27, 2025
hep-thcond-mat.stat-mechcond-mat.str-elQuantum Physics
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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.