RPA ground state correlations from perturbation theory

M. Tohyama, S. Takahara, Peter Schuck

P.J. Ellis

E. Krotscheck

We study the connections between the chain summations of variational theories of Fermi fluids and those generated by ring-diagram summations in the correlated-basis-functions (CBF) perturbation theory. The effective interactions of CBF theory and the random-phase-approximation (RPA) equations in the correlated basis are rewritten in an irreducible form. We discuss local approximations to the irreducible vertex which are sympathetic with the use of variational wave functions. They allow contact to be made with conventional formulations of the RPA, to weak-coupling, pseudopotential, or "local-screening" theories. Our studies lead also to consistency requirements between variational calculations of ground-state properties and the effective interactions used in CBF theory.

Fabio Caruso, Daniel R. Rohr, Maria Hellgren +4 more

For the paradigmatic case of H(2) dissociation, we compare state-of-the-art many-body perturbation theory in the GW approximation and density-functional theory in the exact-exchange plus random-phase approximation (RPA) for the correlation energy. For an unbiased comparison and to prevent spurious starting point effects, both approaches are iterated to full self-consistency (i.e., sc-RPA and sc-GW). The exchange-correlation diagrams in both approaches are topologically identical, but in sc-RPA they are evaluated with noninteracting and in sc-GW with interacting Green functions. This has a profound consequence for the dissociation region, where sc-RPA is superior to sc-GW. We argue that for a given diagrammatic expansion, sc-RPA outperforms sc-GW when it comes to bond breaking. We attribute this to the difference in the correlation energy rather than the treatment of the kinetic energy.

Satoshi Takahara, M. Tohyama, Peter Schuck

The ground states and excited states of the Lipkin model Hamiltonian are calculated using a new theoretical approach that has been derived from an extended time-dependent Hartree-Fock theory known as the time-dependent density-matrix (TDDM) theory. TDDM theory 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.

João da Providência