Abstract
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.
Highlights
The study of phase transitions in quantum systems is a topic of present interest, usually referred to as quantum phase transitions (QPT) [1–3]
We propose the use of the inverse participation ratio (IPR) and the Rényi entropy as other good markers for the critical point
We have studied a two-level model for the coexistence of atoms and diatomic molecules
Summary
The study of phase transitions in quantum systems is a topic of present interest, usually referred to as quantum phase transitions (QPT) [1–3]. Particular Hamiltonians based on algebraic structures that are exactly solvable have been proposed, such as the Lipkin [10], the Bose-Hubbard [11], the Jaynes–Cummings, the Tavis–Cummings and the Dicke models [12–14], just to cite a few of them. These models present specific dynamical symmetries that correspond to different equilibrium configurations of the system in the ground state. We propose the use of the inverse participation ratio (IPR) and the Rényi entropy as other good markers for the critical point
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