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