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Physics Letters A

The two-level Lipkin model solution within the RPA approach for deformed fermions

Eduardo I. Duzzioni, José Ricardo Marinelli

Published May 13, 2004• 4 citations
Publisher
DOI
10.1016/j.physleta.2004.04.063

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The usefulness of the quon expansion to treat Pauli principle violations and many-body correlations in many-fermion systems is investigated within two models, namely, the Lipkin and the two level pairing models. The q deformation parameter of the quon algebra is fixed through a dynamical criterion. The spectra obtained are compared with the random-phase approximation (RPA), usual boson expansion, and exact results. The quonic expansion is shown to take into account correlations which are not included either in the second order boson expansion or in the RPA approach.
We compute the energy functional of a three-level Lipkin model via a Legrendre transform and compare exact numerical results with analytical solutions obtained from the random phase approximation (RPA). Except for the region of the phase transition, the RPA solutions perform very well. We also study the case of three nondegenerate levels and again find that the RPA solution agrees well with the exact numerical result. For this case, the analytical results give us insight into the form of the energy functional in the presence of symmetry-breaking one-body potentials.