Estudio de las transiciones de fase cuánticas de estado fundamental y de estados excitados en el límite bidimensional del modelo de vibronesaplicación al espectro de flexión molecular

Abstract

The study of the molecular structure is very relevant in many aspects of physics. In particular, in this eld, classical, semiclassical, and quantum methods are currently employed. In the present PhD memory, problems of relevance in such a eld are studied using models based on Lie algebras. The main advantage of the algebraic models is their abstract character, that allows for their application to widely di erent physical systems. Across the many possible problems in the description of molecular structure, the present work pays heed to the vibrational bending motion. Due to the planar nature of this molecular degree of freedom, most calculations in this work are carried out in the two-dimensional (2D) limit of the vibron model. This model has been used for the description of molecular bending spectra since its introduction by Iachello and Oss in 1996 obtaining successful results. One of the aims of this thesis is to accomplish ts to experimental band origins with spectroscopy accuracy, obtaining in this way an accurate prediction of yet unobserved levels. To achieve this task, interactions up to four-body are taken into account and both Fortran90 and Python codes have been developed to carry out ts to experimental data using this extended Hamiltonian. Working in this direction, to deal with the bent-to-linear transition of non-rigid molecules is inevitable. This transition has been studied with a simple model Hamiltonian under the 2D vibron model framework. The model Hamiltonian exhibits many features of interest, e.g. a ground-state quantum phase transition and an excited-state quantum phase transition. In addition to the introduction of a four-body Hamiltonian for the calculations, the present memory extends the use of the quantum delity susceptibility, borrowed from Quantum Information and traditionally used to characterize ground-state quantum phase transitions, to the realm of excited states. The quantum delity susceptibility is used together with the participation ratio, the Birge-Sponer plot or ground-state quantum phase transition order parameter to characterize excited-state quantum phase transitions in several Hamiltonians. The next problem studied from an algebraic perspective is the isomerization reaction in the [H,C,N] system. The isomerization transition between HCN and HNC has exhibited quantum phase transitions features between two symmetric excited-state phases due to the linear con guration of both isomers. This issue revealed a new excited-state quantum phase transition in the symmetric phase of the anharmonic model Hamiltonian. This transition is characterized in this zone together with an in-depth study of its extension to the broken-symmetry phase. This memory also pays heed to the possibility of coexistence of symmetric and broken-symmetry minima. Such coexistence is impossible in a two-body algebraic model Hamiltonian, but the inclusion of three- and four-body terms allows for the occurrence of rst-order quantum phase transitions and provides a large gamut of systems. In particular, a three-body operator coupled with the one- and two-body Hamiltonian has been analyzed. The ground state of this Hamiltonian presents a rst-order quantum phase transition and a rich excited spectrum. So far, only static features of the 2D vibron model has been examined. Taking advantage of the out-of-time-ordered correlators boom, a quantity introduced in the study of quantum chaos and quantum information scrambling, the dynamic in the model Hamiltonian has been studied through this tool. The time dependence of these correlators as well as its stationary value have been analyzed, with special emphasis in the shorttime limit, given by the Ehrenfest's time, and the in uence of the transition to linearity on this quantity.