Report Correlation Team meeting number zero
This is a brief report of the correlation meeting number 0 held in Palaiseau on 17-18 January 2011.
This meeting was the pilot project and the basis of the organization of the first real meeting that took place 3 months later in Palaiseau.
Participants: Arjan Berger, Silke Biermann, Fabio Caruso, Matteo Gatti, Lucia Reining, Patrick Rinke, Pina Romaniello, Claudia Rödl, Francesco Sottile
List of possible discussion topics for the meeting:
1. Satellites - (how do we calculate them; how good are the calculations; how do we interpret them; what is missing)
- Self-consistent GW vs. cumulant expansion
- Is it meaningful to use methods derived from the homogeneous electron gas for finite systems?
- Fully self-consistent GW
- Why are we interested in satellites? Why might the DMFT community be interested in satellites and how are they describe there? Is the interpretation the same in different communities?
- H+2 in the atomic limit: 2 addition energies of which one is a satellite and the other one a quasiparticle; H +H+: 2 quasiparticle peaks
- Experiments: what is measured?
2. Gap problem- (how do we open the gap; when and why don't our approximations work)
- DMFT correlation problem: is there a system where the gap is opened by correlation?
- unoccupied d/f states too high in GW?
- Phonons in principle reduce the band gap? (Interaction with the phonon collaboration team)
3. Magnetism + spin-symmetry breaking
4. Which are the benchmark systems for which GW results are well-established (and which level of refinement)? And which ones are those for DMFT?
1 Magnetism + symmetry breaking
Presentation by Claudia Rödl. Discussion on MnO and NiO. Within the rock-salt structure, LDA/GGA correctly predicts the AFII magnetic ordering to be the ground state of MnO. Studying other chemical structures (wurtzite, zinc-blende) in LDA/GGA, one finds them to be energetically favored compared to rock-salt which is in contradiction to experiment. HF and HSE03 cannot cure the problem; GGA+U can, if U>~eV. U is in principle a screened-exchange contribution. U means different things in different siutations (ground-state total energy, band gap, ...). Therefore, the ``appropriate'' values of U can differ depending on the quantity one is interested in. What do we miss in these functionals? Which correlation contributions are the important ones? For detailed results confer Phys. Rev. B 82, 165109 (2010). Everything comes out correctly for NiO.
2 Self-consistent GW for finite systems
Presentation by Fabio Caruso. Self-consistent GW: spectral function and total energy. The Green's function is obtained by iterative solution of the Dyson's equation in imaginary frequency with the fully screened interaction (sc-GW) and with screening fixed at the RPA level (sc-GW0). In both cases the integrated spectral function is independent of the functional of the preliminary SCF calculation. Moreover, the correct number of particle is reproduced. Tested on a set of 20 molecules, the ionization energies calculated from sc-GW and sc-GW0 improve the agreement with experiments as compared to G0W0@LDA, with a slightly better performance for sc-GW0. Preliminary study on Na cluster: a weak satellite feature in the valence band is observed in the G0W0 spectrum, which disappears for sc-GW. This is in analogy with previous work on the homogeneous electron gas (Phys. Rev. B 57, 2108 (1998)) where a strong loss in the intensity of the plasmon satellite peak characterises the sc-GW spectrum, while this does not happen in sc-GW0. Total energy in sc-GW: is calculated with the Galitskii-Migdal formula and gives values that are comparable to MP2 calculations for atoms and dimers.
3 Satellites in Si
Presentation by Lucia Reining. Photoemission measurements at high energy (source energy: 800 eV) really show the valence spectral function; shortcoming: no angular resolved, i.e. spectrum integrated over the Brillouin zone. In the new measurements on Si (done by Fausto Sirotti) one clearly sees plasmon replicas. These replicas are well-described by the cumulant expansion, which is derived for core spectroscopy using a polaron model (electrons interacting with plasmons), whereas are completely missing in GW. The cumulant can be also derived starting from the equation of motion for G and using approximations that are equivalent to those used to derive the cumulant in the polaron model. Is the cumulant OK for finite systems?Here we can have only a finite number of plasmons, whereas the cumulant produces an infinite number. Which approximation makes the cumulant wrong for finite systems? The linearization of the Hartree potential? Or the fact that levels are decoupled?