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

Institute of Experimental and Applied Physics, Czech Technical University in Prague, Horská 3a/22, 128 00 Prague 2, Czech Republic

E-mail Address: jun.terasaki@cvut.cz

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A. Smetana

Institute of Experimental and Applied Physics, Czech Technical University in Prague, Horská 3a/22, 128 00 Prague 2, Czech Republic

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F. Šimkovic

Institute of Experimental and Applied Physics, Czech Technical University in Prague, Horská 3a/22, 128 00 Prague 2, Czech Republic

Department of Nuclear Physics and Biophysics, Comenius University, Mlynská Dolina F1, SK-842 48 Bratislava, Slovakia

Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia

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M. I. Krivoruchenko

Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia

Institute for Theoretical and Experimental Physics, B. Cheremushkinskaya 25, 117218 Moscow, Russia

Department of Nano-, Bio-, Information, and Cognitive Technologies, Moscow Institute of Physics and Technology, 9 Institutskii per. 141700 Dolgoprudny, Moscow Region, Russia

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https://doi.org/10.1142/S0218301317500628Cited by:4 (Source: Crossref)

Abstract

It is shown that the random-phase approximation (RPA) method with its nonlinear higher generalization, which was previously considered as approximation except for a very limited case, reproduces the exact solutions of the Lipkin model. The nonlinear higher 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 $N = 2$ $N = 2$ and, numerically, for $N = 8$ $N = 8$ . This finding indicates that the nonlinear higher RPA is equivalent to the exact Schrödinger equation, which opens up new possibilities for realistic calculations in many-body problems.

Keywords:

PACS: 21.60.Jz, 71.10.-w

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