Reproduction of exact solutions of Lipkin model by nonlinear random-phase approximation

Abstract

It is shown that the random-phase approximation (RPA) method with its nonlinear generalization, which was previously considered as approximation, reproduces the exact solutions of the Lipkin model. The nonlinear RPA is based on an equation nonlinear on eigenvectors and includes many-particle-many-hole components in the creation operator of the excited states. We demonstrate the exact character of solutions analytically for the particle number $N$ = 2 and, numerically, for $N$ = 20. This finding indicates that the nonlinear RPA is equivalent to the exact Schrödinger equation, which opens up new possibilities for realistic calculations in many-body problems.

17 pages, 9 figures

References in corpus (1)

• Status and Future of Nuclear Matrix Elements for Neutrinoless Double-Beta Decay: A Review

Cited by in corpus (3)

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• Combining symmetry breaking and restoration with configuration interaction: extension to z-signature symmetry in the case of the Lipkin Model
• A possible trial beyond the conventional random phase approximation for the su(2)-Lipkin model including the case of non-closed shell system