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 chaotic system with a quantum group global symmetry. The example is a spin chain with a next-to-nearest interaction term. We show the chaotic behavior of the system by studying the Eigenvalue statistics. The spin chain is nonunitary but PT symmetric and, in addition to exhibiting chaos, exhibits an interesting transition after which the eigenvalues become complex.

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• Quantum chaos
• 1-dimensional spin chains
• Conformal symmetry
• PT-symmetry
• Quantum group symmetries
• Integrable systems
• Quantum spin chains