We study the quantum phase transitions of a model that describes theinterconversion of interacting bosonic atoms and molecules. Using a classicalanalysis, we identify a threshold coupling line separating a molecular phaseand a mixed phase. Through studies of the energy gap, von Neumann entanglemententropy, and fidelity, we give evidence that this line is associated to aboundary line in the ground-state phase diagram of the quantum system.

Quantum phase transitions in an interacting atom-molecule boson model