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A Quantum Phase Transition (QPT) in a simple model that describes thecoexistence of atoms and diatomic molecules is studied. The model, that isbriefly discussed, presents a second order ground state phase transition in thethermodynamic (or large particle number) limit, changing from a molecularcondensate in one phase to an equilibrium of diatomic molecules-atoms incoexistence in the other one. Usual markers for this phase transition are theground state energy and the expectation value of the number of atoms (or,alternatvely, the number of molecules) in the ground state. In this work, othermarkers for the QPT as the Inverse Participation Ratio (IPR) and, particularly,the R\'enyi entropy are analysed and proposed as QPT markers. Both magnitudespresent abrupt changes at the critical point of the QPT.

Entropies and IPR as Markers for a Phase Transition in a Two-Level Model for Atom-Diatomic Molecule Coexistence