Abstract
We characterize excited state quantum phase transitions in the two dimensional limit of the vibron model with the quantum fidelity susceptibility, comparing the obtained results with the information provided by the participation ratio. As an application, we locate the eigenstate closest to the barrier to linearity and determine the linear or bent character of the different overtones for particular bending modes of six molecular species. We perform a fit and use the optimized eigenvalues and eigenstates in three cases and make use of recently published results for the other three cases.
Highlights
The study of bending vibrational degrees of freedom has been fostered due to their twodimensional nature and the existence of two well-defined physical limits –linear and bent configurations, together with intermediate configurations –quasilinear species, characterized by a large amplitude motion that makes them rich in spectroscopic signatures [1]
We extend the concept of quantum fidelity susceptibility (QFS) beyond the ground state, to the realm of excited states, and we use this magnitude as a probe to locate excited states in the 2DVM with respect to the separatrix line between different excited state quantum phase transitions (ESQPTs) phases
The main contribution of this work is the study of an ESQPT making use of the quantum fidelity susceptibility
Summary
The study of bending vibrational degrees of freedom has been fostered due to their twodimensional nature and the existence of two well-defined physical limits –linear and bent configurations–, together with intermediate configurations –quasilinear species–, characterized by a large amplitude motion that makes them rich in spectroscopic signatures [1]. We extend the concept of QFS beyond the ground state, to the realm of excited states, and we use this magnitude as a probe to locate excited states in the 2DVM with respect to the separatrix line between different ESQPT phases We will apply this to the results obtained in the fit of Hamiltonian (11) to several molecular species obtaining an unambiguous assignment of the excited states to a given basis. The QFS provides a trustworthy and basis-independent method to locate states with respect to the high level density separatrix lines that characterize ESQPTs. The case (10) is a simple one, but we show how to use the QFS in a more general case, with an application to the bending wavefunctions obtained from the fit of spectroscopic parameters from an algebraic Hamiltonian including up to four-body interactions to reported vibrational bending band origins for different molecular species.
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