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arXiv:nucl-th/0103012 · Journal of Physics G Nuclear and Particle Physics

Quasiparticle random-phase approximation with an optimal ground state

F. Šimkovic, M. Šmotlák, Apolodor Aristotel Raduta

Published Jul 2, 2001• 6 citations
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Abstract

A new quasiparticle random-phase approximation approach (QRPA) is presented. The corresponding ground state is variationally determined and exhibits a minimum energy. New solutions for the ground state, some with spontaneously broken symmetry, of a solvable Hamiltonian are found. A non-iterative procedure to solve the nonlinear QRPA equations is used and thus all possible solutions are found. These are compared with the exact results as well as with the solutions provided by other approaches.

DOI
10.1088/0954-3899/27/8/305

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A method is proposed to improve the treatment of the ground-state correlations in a finite Fermi system compared with the standard random phase approximation (RPA) or earlier suggested renormalized RPA. The correlations lead to nonzero quasiparticle occupancies in the ground state. The method employs modified quasiparticles obtained by a canonical transformation of usual quasiparticles explicitly involving the quasiparticle occupation numbers. A set of equations is derived, which allows one to determine these occupation numbers along with the RPA modes. The formalism is illustrated with the Lipkin-Meshkov-Glick model, and a model for superconducting pairing at a finite temperature. With the new approach, the ground-state correlations are significantly reduced, the energy of the first excited state becomes closer to the exact solution around the region where the RPA collapses, and the superconducting gap monotonously decreases instead of the sharp phase transition. We discuss the effective equivalence of the interaction effects and variation of temperature for the ground-state correlations.
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A connection between the random-phase-approximation (RPA) total energy ERPA{E}_{\text{RPA}}ERPA​ and the GWGWGW quasiparticle energy ϵGW{ϵ}_{GW}ϵGW​ has been pointed out. More specifically we show that: $\ensuremath{\delta}{E}_{\text{RPA}}(N)/\ensuremath{\delta}N={ϵ}_{GW}$, where NNN is the total number of electron. The variational property of the RPA total energy is also discussed and the variational equations for the orbital wave functions are derived. We argue that the RPA formalism is a method which can provide both accurate ground-state energies and single quasiparticle energies.