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In most cases, excited state quantum phase transitions can be associated withthe existence of critical points (local extrema or saddle points) in a system'sclassical limit energy functional. However, an excited-state quantum phasetransition might also stem from the lowering of the asymptotic energy of thecorresponding energy functional. One such example occurs in the 2D limit of thevibron model, once an anharmonic term in the form of a quadratic bosonic numberoperator is added to the Hamiltonian. The study of this case in thebroken-symmetry phase was presented in Phys. Rev. A. 81 050101 (2010). In thepresent work, we delve further into the nature of this excited-state quantumphase transition and we characterize it in the, previously overlooked,symmetric phase of the model making use of quantities such as the effectivefrequency, the expected value of the quantum number operator, the participationratio, the density of states, and the quantum fidelity susceptibility. Inaddition to this, we extend the usage of the quasilinearity parameter,introduced in molecular physics, to characterize the phases in the spectrum ofthe anharmonic 2D limit of the vibron model and a down-to-earth analysis hasbeen included with the characterization of the critical energies for the linearisomers HCN/HNC.

Anharmonicity-induced excited-state quantum phase transition in the symmetric phase of the two-dimensional limit of the vibron model