LAUSR

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 takes place in the 2D 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. Quantum phase transitions (QPTs) are zero-temperature phase transitions that occur when a quantum system ground state undergoes an abrupt variation when a Hamiltonian interaction parameter, named control parameter, goes through a critical value. Such transitions have been observed in numerous quantum systems in different fields: quantum optics, condensed-matter, atomic, nuclear, and molecular systems [1]. In the case of algebraic models, based on Lie algebras and useful in studies of molecular [2, 3], nuclear [4], and hadronic structure [5], the different phases can be mapped to the system dynamical symmetries. A general classification of ground state QPTs in algebraic models can be found in [6] and for an extended treatment see the reviews [7–9] and references therein. In the present work we deal with the two-dimensional limit of the vibron model (2DVM), introduced by Iachello and Oss for the treatment of bending molecular vibrations [10] as collective bosonic excitations (vibrons). The dynamical algebra of the systems is u(3), with two possible dynamical symmetries, associated with the u(2) and so(3) subalgebras and known as the cylindrical and anharmonic oscillator dynamical symmetries [11]. The two subalgebra chains end up in the system symmetry algebra, so(2), which denotes the conservation of the vibrational angular momentum in the molecular case, which lies perpendicular to the plane of the bending motion ∗ Miguel Carvajal: [email protected]