Unexpected features of quantum degeneracies in a pairing model with two integrable limits

TL;DR

This paper investigates how quantum degeneracies, such as level crossings and exceptional points, reveal integrability in a pairing model with two limits, showing that these features can uniquely identify quantum integrability.

Contribution

It demonstrates that level crossings and the number of exceptional points serve as signatures of quantum integrability in models with multiple parameter-dependent integrals of motion.

Findings

Level crossings indicate quantum integrability in complex-extended Hamiltonians.

Integrability correlates with fewer exceptional points in the model.

Quantum degeneracies can uniquely characterize integrability in small Hilbert spaces.

Abstract

The evolution pattern of level crossings and exceptional points is studied in a non-integrable pairing model with two different integrable limits. One of the integrable limits has two independent parameter-dependent integrals of motion. We demonstrate, and illustrate in our model, that quantum integrability of a system with more than one parameter-dependent integral of motion is always signaled by level crossings of a complex-extended Hamiltonian. We also find that integrability implies a reduced number of exceptional points. Both properties could uniquely characterize quantum integrability in small Hilbert spaces.