Chaos in Systems with Quantum Group Symmetry

TL;DR

This paper presents an example of a non-integrable, chaotic quantum spin chain with quantum group symmetry, demonstrating chaos through eigenvalue statistics and revealing a transition to complex eigenvalues in a PT-symmetric, non-unitary system.

Contribution

It provides the first explicit example of a quantum system with quantum group symmetry exhibiting chaos, challenging the notion that such symmetries imply integrability.

Findings

The spin chain shows chaotic eigenvalue statistics.

The system undergoes a transition to complex eigenvalues.

The model is PT-symmetric and non-unitary.

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.