Entropies and IPR as Markers for a Phase Transition in a Two-Level Model for Atom–Diatomic Molecule Coexistence
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Quantum phase transitionsExactly solvable modelsInverse participation ratioRényi entropy
Baena, I.; Pérez-Fernández, P.; Rodríguez-Gallardo, M.; Arias, J.M. Entropies and IPR as Markers for a Phase Transition in a Two-Level Model for Atom–Diatomic Molecule Coexistence. Entropy 2022, 24, 113. [https://doi.org/10.3390/e24010113]
SponsorshipConsejería de Economía, Conocimiento, Empresas y Universidad, Junta de Andalucía; Secretaría de Estado de Investigacion, Desarrollo e Innovacion FQM-160, MCIN/AEI/10.13039/501100011033, PID2019-104002GB-C22, PID2020-114687GB-I00; European Regional Development Fund US-1380840
A quantum phase transition (QPT) in a simple model that describes the coexistence of atoms and diatomic molecules is studied. The model, which is briefly discussed, presents a second-order ground state phase transition in the thermodynamic (or large particle number) limit, changing from a molecular condensate in one phase to an equilibrium of diatomic molecules–atoms in coexistence in the other one. The usual markers for this phase transition are the ground state energy and the expected value of the number of atoms (alternatively, the number of molecules) in the ground state. In this work, other markers for the QPT, such as the inverse participation ratio (IPR), and particularly, the Rényi entropy, are analyzed and proposed as QPT markers. Both magnitudes present abrupt changes at the critical point of the QPT.