Chaos in Systems with Quantum Group Symmetry
High Energy Physics - Theory
2026-01-27 v2 Statistical Mechanics
Strongly Correlated Electrons
Quantum Physics
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.
Cite
@article{arxiv.2510.23247,
title = {Chaos in Systems with Quantum Group Symmetry},
author = {Victor Gorbenko and Aleksandr Zhabin},
journal= {arXiv preprint arXiv:2510.23247},
year = {2026}
}
Comments
v1: 17 pages, 7 figures; v2: references added, Appendix B on complex distributions added