Description of Pairing correlation in Many-Body finite systems with density functional theory

Abstract

Different steps leading to the new functional for pairing based on natural orbitals and occupancies proposed in ref. [D. Lacroix and G. Hupin, arXiv:1003.2860] are carefully analyzed. Properties of quasi-particle states projected onto good particle number are first reviewed. These properties are used (i) to prove the existence of such a functional (ii) to provide an explicit functional through a 1/N expansion starting from the BCS approach (iii) to give a compact form of the functional summing up all orders in the expansion. The functional is benchmarked in the case of the picked fence pairing Hamiltonian where even and odd systems, using blocking technique are studied, at various particle number and coupling strength, with uniform and random single-particle level spacing. In all cases, a very good agreement is found with a deviation inferior to 1% compared to the exact energy.

14 pages, 9 figures

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• Projected Quasi-particle Perturbation theory
• Combining symmetry breaking and restoration with configuration interaction: a highly accurate many-body scheme applied to the pairing Hamiltonian
• Possibility of Electron Pairing in Small Metallic Nanoparticles
• Thermodynamics of small superconductors with fixed particle number
• On the formulation of functional theory for pairing with particle number restoration
• On the description of two-particle transfer in superfluid systems
• Density Functional Theory with Spatial-Symmetry Breaking and Configuration Mixing
• Variational Principle Directly on the Coherent Pair Condensate. I. the BCS Case
• Occupation number-based energy functional for nuclear masses
• Functional approach for pairing in finite systems: How to define restoration of broken symmetries in Energy Density Functional theory ?