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We study the structure of the eigenstates and the dynamics of a system that undergoes an excited-state quantum phase transition (ESQPT). The analysis is performed for two-level pairing models characterized by a U(n + 1) algebraic structure. They exhibit a second-order phase transition between two limiting dynamical symmetries represented by the U(n) and SO(n + 1) subalgebras. They are, or can be mapped onto, models of interacting bosons. We show that the eigenstates with energies very close to the ESQPT critical point, FESQPT, are highly localized in the U(n) basis. Consequently, the dynamics of a system initially prepared in a U(n)-basis vector with energy ᵋ ~ EESQPT may be extremely slow. Signatures of an ESQPT can therefore be found in the structures of the eigenstates and in the speed of the system evolution after a sudden quench. Our findings can be tested experimentally with trapped ions. [ABSTRACT FROM AUTHOR]

A simple and yet powerful approach for modeling the structure of endohedrally confined diatomic molecules is introduced. The theory, based on a u(4)⊕u(3) dynamical algebra, combines u(4), the vibron model dynamical algebra, with a u(3) dynamical algebra that models a spherically symmetric three-dimensional potential. The first algebra encompasses the internal rotovibration degrees of freedom of the molecule, while the second takes into account the confined molecule center-of-mass degrees of freedom. A resulting subalgebra chain is connected to the underlying physics and the model is applied to the prototypical case of H2 caged in a fullerene molecule. The spectrum of the supramolecular complex H2@C60 is described with a few parameters, and predictions for not yet detected levels are made. Our fits suggest that the quantum numbers of a few lines should be reassigned to obtain better agreement with data. [ABSTRACT FROM AUTHOR]

Excited-state quantum phase transitions (ESQPTs) are generalizations of quantum phase transitions to excited levels. They are associated with local divergences in the density of states. Here, we investigate how the presence of an ESQPT can be detected from the analysis of the structure of the Hamiltonian matrix, the level of localization of the eigenstates, the onset of bifurcation, and the speed of the system evolution. Our findings are illustrated for a Hamiltonian with infinite-range Ising interaction in a transverse field. This is a version of the Lipkin-Meshkov-Glick (LMG) model and the limiting case of the one-dimensional spin-1/2 system with tunable interactions realized with ion traps. From our studies for the dynamics, we uncover similarities between the LMG and the noninteracting XX models. [ABSTRACT FROM AUTHOR]