Energy functional for the three-level Lipkin model

Abstract

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 non-degenerate 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.

6 pages, 5 figures

References in corpus (8)

• Local Density Functional Theory for Superfluid Fermionic Systems: The Unitary Gas
• Density-functional theory for fermions in the unitary regime
• Non-empirical pairing functional
• Density Functional Theory for a Confined Fermi System with Short-Range Interaction
• The Kinetic Energy Density in Kohn-Sham Density Functional Theory
• Effective Field Theory for Dilute Fermions with Pairing
• Single-Particle Properties from Kohn-Sham Green's Functions
• Density-functional theory for the pairing Hamiltonian

Cited by in corpus (1)

• Density Matrix Functional Theory for the Lipkin model