Quantum Phase Transitions in Coupled Systems : an application of Catastrophe Theory

Abstract

Two-fluid algebraic models are of great interest in the context of quantum phase transition in nuclei. We intend to study the phase diagram of a two-fluid Lipkin model that resembles a nuclear proton-neutron interacting boson model Hamiltonian. We study the mean-field energy surface of a consistent-Q like two-fluid Lipking Hamiltonian and we compare with exact results coming from a direct diagonalization. We obtain the phase diagram of the model, identifying the order of the different phase-transition lines and surfaces using a Catastrophe Theory analysis. We found that there are two first order surfaces, one separating the spherical and the deformed shape, while the other separating the ``oblate'' and the "prolate" phases. We also found a second order line finishing in a third order phase transition point.