Extended RPA with ground-state correlations

Tohyama, Mitsuru; Takahara, Satoshi; Schuck, Peter

doi:10.1140/epja/i2003-10199-6

Cited by 12 publications

(22 citation statements)

References 33 publications

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“…They have been recently discussed in several works by Tohyama and co-workers. [23][24][25][26][27] They are based on a systematic truncation of the hierarchy of the equations of motion for the one-body and two-body den-sity matrix. The equations one gets in such a way are more general than the RPA and SRPA ones, the main difference being that many more configurations than 2p −2h and 1p −1h appear.…”

Section: Introductionmentioning

confidence: 99%

Second random phase approximation studies in metallic clusters

Gambacurta

Catara

2009

Phys. Rev. B

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We study collective states in metallic clusters within the second random phase approximation ͑RPA͒ including all kinds of couplings among all one particle-one hole and two particle-two hole configurations. The calculations are done in the jellium approximation. The coupling of one particle-one hole configurations with the two particle-two hole ones strongly pushes down the multipole strength distribution, especially for the dipole case, with respect to RPA. The inclusion of the coupling of the two particle-two hole configurations among themselves enhances this behavior also for the collective states whose description within RPA is widely accepted as satisfactory. Some possible origins of these unpleasant results are discussed. In particular, the need for a better treatment of short-range correlations is underlined.A mnij,pqkl = ͗HF͉͓a i † a j † a n a m ,͑H,a p † a q † a l a k ͔͉͒HF͘, ͑12͒B mnij,pqkl = − ͗HF͉͓a i † a j † a n a m ,͑H,a k † a l † a q a p ͔͉͒HF͘. ͑15͒Therefore, in SRPA, the QBA is still used. As a consequence of the use of the ͉HF͘ state in the evaluation of the SRPA matrices we obtain, in particular, 14,15

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Section: Introductionmentioning

confidence: 99%

Second random phase approximation studies in metallic clusters

Gambacurta

Catara

2009

Phys. Rev. B

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“…On the other hand, the time-dependent density-matrix (TDDM) theory [2], which we have developed in the past decade, incorporates the effects of two-body correlations into TDHF theory, and its small amplitude limit (STDDM) [3] becomes a natural extension of RPA, which includes two-body amplitudes and also the effects of ground-state correlations: The correlated ground state is obtained as a stationary solution of the TDDM equations. We have recently applied this TDDM plus STDDM approach to study the ground states and low-lying quadrupole states in unstable oxygen isotopes [4,5]. Although those results are quite encouraging, the validity of the TDDM plus STDDM approach should be tested in further applications.…”

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confidence: 99%

“…The detailed expressions of S͑E͒ for one-body and two-body excitation operators are given in Ref. [5]. The Lipkin model [7] describes an N-fermion system with two N-fold degenerate levels with energies ⑀ / 2 and −⑀ /2, respectively.…”

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confidence: 99%

“…The Hamiltonian matrix in the STDDM approach [Eq. (3)] is not Hermitian in general [5,8], and as a result, there is a possibility that some eigenvalues become complex. However, the Hamiltonian in the Lipkin model is so simple that all eigenvalues are real and that the strength functions are positive definite.…”

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confidence: 99%

“…(25) of Ref. [5] for a detailed explanation of the prescription.] We call this version of the STDDM approach the mSTDDM approach.…”

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confidence: 99%

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Extended RPA with ground-state correlations in a solvable model

2004

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The ground states and excited states of the Lipkin model hamiltonian are calculated using a new theoretical approach which has been derived from an extended time-dependent Hartree-Fock theory known as the time-dependent density-matrix theory (TDDM). TDDM enables us to calculate correlated ground states, and its small amplitude limit (STDDM), which is a version of extended RPA theories based on a correlated ground state, can be used to calculate excited states. It is found that this TDDM plus STDDM approach gives much better results for both the ground states and the excited states than the Hartree-Fock ground state plus RPA approach.Comment: 4 pages, 4 figure

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Progress in many-body theory with the equation of motion method: Time-dependent density matrix meets self-consistent RPA and applications to solvable models

Schuck¹,

Tohyama²

2016

Phys. Rev. B

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The Bogoliubov-Born-Green-Kirkwood-Yvon or Time-Dependent Density Matrix (TDDM) hierarchy of equations for higher density matrices is truncated at the three body level in approximating the three body correlation function by a quadratic form of two body ones, closing the equations in this way. The procedure is discussed in detail and it is shown in non-trivial model cases that the approximate inclusion of three body correlation functions is very important to obtain precise results. A small amplitude approximation of this time dependent nonlinear equation for the two body correlation function is performed (STDDM*-b) and it is shown that the one body sector of this generalised non-linear second RPA equation is equivalent to the Self-Consistent RPA (SCRPA) approach which had been derived previously by different techniques. It is discussed in which way SCRPA also contains the three body correlations. TDDM and SCRPA are tested versus exactly solvable model cases.

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Extended RPA with ground-state correlations

Cited by 12 publications

References 33 publications

Second random phase approximation studies in metallic clusters

Second random phase approximation studies in metallic clusters

Extended RPA with ground-state correlations in a solvable model

Progress in many-body theory with the equation of motion method: Time-dependent density matrix meets self-consistent RPA and applications to solvable models

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