The role of the small-norm amplitudes in extended random-phase approximation (RPA) theories such as the particle-particle and hole-hole components of one-body amplitudes and the twobody amplitudes other than two-particle/two-hole components are investigated for the onedimensional Hubbard model using an extended RPA derived from the time-dependent density matrix theory.It is found that these amplitudes cannot be neglected in strongly interacting regions where the effects of ground-state correlations are significant.............The role of the small-norm amplitudes in extended random-phase approximation (RPA) theories such as the particle-particle and hole-hole components of one-body amplitudes and the twobody amplitudes other than two-particle/two-hole components are investigated for the onedimensional Hubbard model using an extended RPA derived from the time-dependent density matrix theory.It is found that these amplitudes cannot be neglected in strongly interacting regions where the effects of ground-state correlations are significant.............

arXiv:1708.07219Progress of Theoretical and Experimental PhysicsAug 22, 20172 citations

The extension of the random phase approximation in the many-body theory

S. I. Kubarev

Physics Letters AAug 1, 19742 citations

Effects of ground-state correlations on magnetic dipole excitations in $^{40}$ CaEffects of ground-state correlations on magnetic dipole excitations in $^{40}$Ca

M. Tohyama

The effects of ground-state correlations on the magnetic dipole excitations in $^{40}$ Ca are studied using an extended random phase approximation (ERPA) derived from the time-dependent density-matrix theory. Comparison is made with other extended RPA approaches, the renormalized RPA, the self-consistent RPA and the extended second RPA which also include the effects of ground-state correlations. It is pointed out that direct excitations from two particle - two hole space which are properly treated in ERPA cause strong magnetic dipole transitions in $^{40}$ Ca.The effects of ground-state correlations on the magnetic dipole excitations in $^{40}$Ca are studied using an extended random phase approximation (ERPA) derived from the time-dependent density-matrix theory. Comparison is made with other extended RPA approaches, the renormalized RPA, the self-consistent RPA and the extended second RPA which also include the effects of ground-state correlations. It is pointed out that direct excitations from two particle - two hole space which are properly treated in ERPA cause strong magnetic dipole transitions in $^{40}$Ca.

arXiv:2009.02014Sep 4, 20200 citations

Self-consistent extension of random-phase approximation enlarged beyond particle-hole configurations

D. Gambacurta, F. Catara, M. Grasso

We present a new extension of the random-phase approximation method: the quasiboson approximation is avoided and correlations are included in the ground state without resorting to renormalized operators or renormalized matrix elements; the configuration space is enlarged by considering also elementary excitations corresponding to the annihilation of a particle (hole) and the creation of another particle (hole) on the correlated ground state, together with the particle-hole ones. Two new and relevant advantages of this method with respect to the existing extensions of random-phase approximation are highlighted: (i) the energy weighted sum rules are completely satisfied; (ii) the problem of the existence of nonphysical states in the spectrum, related to the inclusion of particle-particle and hole-hole configurations, is solved: a way to unambiguously disentangle physical from nonphysical states in the excitation spectrum is presented. The method is applied here to a three-level Lipkin model where its quality can be judged by comparing with the exact results. Both advantages (i) and (ii) shall lead to feasible future applications of this extended RPA to several realistic cases.We present a new extension of the random-phase approximation method: the quasiboson approximation is avoided and correlations are included in the ground state without resorting to renormalized operators or renormalized matrix elements; the configuration space is enlarged by considering also elementary excitations corresponding to the annihilation of a particle (hole) and the creation of another particle (hole) on the correlated ground state, together with the particle-hole ones. Two new and relevant advantages of this method with respect to the existing extensions of random-phase approximation are highlighted: (i) the energy weighted sum rules are completely satisfied; (ii) the problem of the existence of nonphysical states in the spectrum, related to the inclusion of particle-particle and hole-hole configurations, is solved: a way to unambiguously disentangle physical from nonphysical states in the excitation spectrum is presented. The method is applied here to a three-level Lipkin model where its quality can be judged by comparing with the exact results. Both advantages (i) and (ii) shall lead to feasible future applications of this extended RPA to several realistic cases.

Physical Review CJul 6, 200910 citations

Three-body problem in the ground-state representation

Augusto González

Few-Body SystemsJan 1, 19930 citations

Effects of ground-state correlations on magnetic dipole excitations in

^{40}

The effects of ground-state correlations on the magnetic dipole excitations in

^{40}

Ca are studied using an extended random phase approximation (ERPA) derived from the time-dependent density-matrix theory. Comparison is made with other extended RPA approaches, the renormalized RPA, the self-consistent RPA and the extended second RPA which also include the effects of ground-state correlations. It is pointed out that direct excitations from two particle - two hole space which are properly treated in ERPA cause strong magnetic dipole transitions in

^{40}

Ca.