Miloslav Znojil

The answer is yes. Via an elementary, exactly solvable crypto-Hermitian example it is shown that inside the interval of admissible couplings the innocent-looking point of a smooth unavoided crossing of the eigenvalues of Hamiltonian $H$ may carry a dynamically nontrivial meaning of a phase-transition boundary or “quantum horizon”. Passing this point requires a change of the physical Hilbert-space metric $\Theta$, i.e., a thorough modification of the form and of the interpretation of the operators of all observables.

http://arxiv.org/abs/1303.4876

Quantum Physics (quant-ph); Mathematical Physics (math-ph)