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

Abstract

As already stated in Phys. Rev. A. 81 050101 (2010), the inclusion of anharmonicity into the 2D vibron model in the form of a quadratic bosonic number operator results in a second excited-state quantum phase transition. Such transition, in the classical limit of the model, can be associated with the lowering of the asymptotic energy of the energy functional. We delve into the nature of the new excited-state quantum phase transition and we characterize it in the previously overlooked symmetric phase of the model (also known as cylindrical oscillator or linear phase).

Excited-State Quantum Phase Transitions in the Anharmonic Lipkin-Meshkov-Glick Model I: Static Aspects

“…1 is the correlation energy diagram for a negative α value. As expected from the results obtained for the 2D limit of the vibron model [27,28], there is a new separatrix that crosses the one associated with the ground state QPT and the degeneracy pattern is more complex. In order to better understand the second separatrix we study the classical limit of the model making use of the spin coherent states formalism [70].…”

“…As previously mentioned, a similar ESQPT in the broken symmetry phase of the 2D limit of the vibron model was studied in Ref. [27] and it has recently been shown to be present in the symmetric phase of the model too [28].…”

“…Inspired by the works Ref. [27,28], we include in the Hamiltonian Eq. (2) an anharmonic term, using a second-order operator on Ŝz ,…”

“…[27], it was shown that the inclusion of anharmonicity in the Hamiltonian results in a second ESQPT in the broken-symmetry phase, that is where the typical spectroscopic signatures of nonrigid molecules are found. More recently, in the pursuit of the description of the transition state in isomerization reactions [16], it has been found that the second ESQPT can also be present in the symmetric phase for sufficiently large values of the anharmonicity and it is not associated with the ground state QPT but it stems from changes in the phase-space boundary of the 2DVM's finite-dimensional Hilbert space [28].…”

“…Our aim is to extend the results obtained for the 2DVM [27,28], to the Lipkin-Meshkov-Glick (LMG) model. This model was introduced in 1965 as a toy model for interacting fermions in nuclear physics, to help assessing the performance of different approximations used on that time in the study of nuclear structure [30][31][32].…”