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

TL;DR

This paper investigates an anharmonicity-induced excited-state quantum phase transition in the symmetric phase of the 2D vibron model, revealing new insights into its nature and critical energies using various quantum and spectral analysis tools.

Contribution

It extends the understanding of excited-state quantum phase transitions by characterizing them in the symmetric phase of the 2D vibron model with anharmonic terms, previously studied only in the broken-symmetry phase.

Findings

Identification of the excited-state quantum phase transition in the symmetric phase.

Characterization of the transition using effective frequency, participation ratio, and fidelity susceptibility.

Determination of critical energies for linear isomers HCN/HNC.

Abstract

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.