Self-consistent RPA and the time-dependent density matrix approach

Abstract : The time-dependent density matrix (TDDM) or BBGKY (Bogoliubov, Born, Green, Kirkwood, Yvon) approach is decoupled and closed at the three-body level in finding a natural representation of the latter in terms of a quadratic form of two-body correlation functions. In the small amplitude limit an extended RPA coupled to an also extended second RPA is obtained. Since including two-body correlations means that the ground state cannot be a Hartree-Fock state, naturally the corresponding RPA is upgraded to Self-Consistent RPA (SCRPA) which was introduced independently earlier and which is built on a correlated ground state. SCRPA conserves all the properties of standard RPA. Applications to the exactly solvable Lipkin and the 1D Hubbard models show good performances of SCRPA and TDDM.
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P. Schuck, M. Tohyama. Self-consistent RPA and the time-dependent density matrix approach. European Physical Journal A, EDP Sciences, 2016, 52 (10), pp.307. ⟨10.1140/epja/i2016-16307-7⟩. ⟨in2p3-01410486⟩

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