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The evolution pattern of level crossings and exceptional points is studied ina non-integrable pairing model with two different integrable limits. One of theintegrable limits has two independent parameter-dependent integrals of motion.We demonstrate, and illustrate in our model, that quantum integrability of asystem with more than one parameter-dependent integral of motion is alwayssignaled by level crossings of a complex-extended Hamiltonian. We also findthat integrability implies a reduced number of exceptional points. Bothproperties could uniquely characterize quantum integrability in small Hilbertspaces.

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