RPA abstracts
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The Selfconsistent Quasiparticle RPA and Its Description of Thermal Pairing Properties in Nuclei
Nguyen Dinh Dang
1 - Heavy-Ion Nuclear Physics Laboratory, Nishina Center for Accelerator-Based Science RIKEN 2-1 Hirosawa, Wako city, 351-0198 Saitama, Japan
2 - Institute for Nuclear Science and Techniques, Vietnam Atomic Energy Commission Hanoi - Vietnam
The Selfconsistent Quasiparticle RPA (SCQRPA) is constructed [1] to study the effects of fluctuations on pairing properties in finite systems. The theory is applied to nuclei at finite temperature [2] and angular momentum [3]. Particle number projection is taken into account within the Lipkin-Nogami method. Several issues such as the smoothing of superfluid-normal phase transition, thermally assisted pairing in hot rotating nuclei, extraction of the nuclear pairing gap using an improved odd-even mass difference are discussed [4]. Finally, a novel approach of embedding the projected SCQRPA eigenvalues in the canonical ensemble (CE) is proposed (the CE-SCQRPA) [5]. Applied to a doubly-folded equidistant multilevel pairing model, the proposed CE-SCQRPA produces results in good agreement with those obtained by using the exact eigenvalues, whenever the latter are possible, and is workable also for large values of particle number (N>14), where the diagonalisation of the pairing Hamiltonian is impracticable.
References
[1] N. Quang Hung and N. Dinh Dang, Phys. Rev. C 76 (2007) 054302 and 77 (2008) 029905(E).
[2] N. Dinh Dang and N. Quang Hung, Phys. Rev. C 77 (2008) 064315.
[3] N. Quang Hung and N. Dinh Dang, Phys. Rev. C 78 (2008) 064315.
[4] N. Quang Hung and N. Dinh Dang, Phys. Rev. C 79 (2009) 054328.
[5] N. Quang Hung and N. Dinh Dang, in preparation
The two faces of RPA: density functional theory and many-body perturbation theory
Xavier Gonze
Unité Physico-Chimie et de Physique des Matériaux (PCPM), Université catholique de Louvain, Place Croix du Sud 1, B-1348 Louvain-la-Neuve, Belgique
The RPA expression for total energy might be derived either within density functional theory, (in the adiabatic-connection fluctuation-dissipation framework, by setting the exchange-correlation kernel to zero), or from many-body perturbation theory (from the Nozières functional in the GW approximation for the self-energy, when the green's function corresponds to an energy-independent one-body Hamiltonian). I will review results in which these two faces of RPA appear. First, the RPA exchange-correlation potential is obtained from a linear-response Sham-Schlüter equation [1,2]. Second, the RPA band gap (I-A expression) corresponds to non-renormalized G_0 W_0 [3]. I will also show that density functional theory within the RPA provides a correct description of bond dissociation for the hydrogen dimer in a spin-restricted Kohn-Sham formalism, i.e., without artificial symmetry breaking, with important static (left-right) correlation [4]. Although exact at infinite separation and accurate near the equilibrium bond length [5], the RPA dissociation curve displays unphysical repulsion at larger but finite bond lengths [4,6].
References
[1] Y.-M. Niquet, M. Fuchs, X. Gonze, J. Chem. Phys. 118, 9504 (2003)
[2] Y.-M. Niquet, M. Fuchs, X. Gonze, Phys. Rev. A 68, 032507 (2003)
[3] Y.-M. Niquet, X. Gonze, Phys. Rev. B 70, 245115 (2004)
[4] M. Fuchs, Y.-M. Niquet, X. Gonze, K. Burke, J. Chem. Phys. 122, 094116 (2005)
[5] M. Fuchs, X. Gonze, Phys. Rev. B 65, 235109 (2002)
[6] M. Fuchs, K. Burke, Y.-M. Niquet, X. Gonze, Phys. Rev. Lett. 90, 189701 (2003)
How approximate is the random phase approximation? Comparing RPA against full configuration-interaction calculations
Calvin W. Johnson
Department of Physics, San Diego State University, USA
I compare the random phase approximation against numerically exact configuration-interaction calculations in the nuclear shell model and find good, not perfect, results. This is of particular importance when one is using a phenomenological interaction. I also discuss the so-called "collapse" of RPA in "phase changes" and illustrate the difference between first- and second-order phase changes and how collapse occurs in only one.
References
[1]
[2]
RPA and coupled cluster theory & some recent results including range separation
Gustavo E. Scuseria
Department of Chemistry and Department of Physics & Astronomy, Rice University, Houston, Texas, USA
The recent realization that the ground-state correlation energy of the random phase approximation (RPA) is intimately connected to an approximate coupled cluster doubles (CCD) model [1], opens interesting avenues for mixing RPA with DFT [2]. I will describe some of the recent work done in our research group on RPA, including applications to van der waals and noncovalent interactions [3], the importance of the reference state [4], a simple second-order approximation [5], and a second-order exchange (SOSX) correction that restores antisymmetry [6].
References
[1] The ground state correlation energy of the Random Phase Approximation from a ring Coupled Cluster Doubles approach, G. E. Scuseria, T. M. Henderson, and D. C. Sorensen, J. Chem. Phys. 129, 231101 (2008).
[2] Long-range-corrected hybrids including random phase approximation correlation, B. G. Janesko, T. M. Henderson, and G. E. Scuseria, J. Chem. Phys. 130, 081105 (2009).
[3] Long-range corrected hybrid functionals including random phase approximation correlation: Application to noncovalent interactions, B. G. Janesko, T. M. Henderson, and G. E. Scuseria, J. Chem. Phys. 131, 034110 (2009).
[4] The role of the reference state in long-range random phase approximation correlation, B. G. Janesko and G. E. Scuseria, J. Chem. Phys. 131, 154106 (2009).
[5] Coulomb-only second-order perturbation theory in long-range-corrected hybrid density functionals, B. G. Janesko and G. E. Scuseria, Phys. Chem. Chem. Phys. 11, 9677 (2009).
[6] Hybrid functionals including random phase approximation correlation and second-order screened exchange, J. Paier, B. G. Janesko, T. M. Henderson, G. E. Scuseria, A. Gruneis, and G. Kresse, J. Chem. Phys. submitted.
== Promising first results with an RPA correlation functional based on the frequency-dependent Kohn-Sham exchange kernel ==
Andreas Görling and Andreas Hesselmann
Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Erlangen, Germany
The random phase approximation (RPA) correlation energy is expressed in terms of the exact local Kohn-Sham (KS) exchange potential and corresponding adiabatic and nonadiabatic exchange kernels for density-functional reference determinants. The approach naturally extends the RPA method in which, conventionally, only Coulomb interactions are included. By comparison with the coupled cluster singles doubles with perturbative triples method it is shown for a set of small molecules that the new RPA method based on the KS exchange kernel yields correlation energies more accurate than RPA on the basis of Hartree-Fock exchange.
References
[1] A. Hesselmann and A. Görling, Mol. Phys., in press.
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