Report on Green’s function methods: the next generation


The main objective of the workshop “Green’s function methods: the next generation”, arrived at its 4-th edition, is to bring together an interdisciplinary audience of researchers dealing with Green’s functions methods and electron correlation. Both fundamental developments and high-end applications are targeted, together with discussions on numerical implementations and their current limitations.

Green’s functions have always played a prominent role in many-body physics. In particular the one-body Green’s function (GF) delivers a wealth of information about a physical system, such as ground-state energy, excitation energies, densities and other measurable quantities. Therefore the development of approximate methods to calculate the one-body GF has been an active research topic in many-body physics since the 60’s, and many routes have been explored in order to find increasingly accurate GFs. A very popular class of methods is based on the iterative solution of an integral equation for the GF containing an effective potential, the so-called self-energy, which needs to be approximated. The well-known GW approximation belongs to this class; this approximation is the method of choice for calculating band structures, but it also shows several shortcomings, such as the wrong description of satellites in photo-emission spectra, in particular in so-called strongly-correlated materials. Therefore more refined levels of approximations are needed to keep the pace with the advances made in experiment. Recently much progress has been made in this direction both by going beyond standard methods and also exploring completely novel routes to calculate GF. A new wave of original ideas, understanding, and solutions, has pervaded the field and was represented in the present workshop.


The workshop was composed of several sessions, through the 4 days (see program below). In each session every speaker was allocated 30 minutes talk, plus 20 minutes of discussions. At the end of each session, extra time was allocated for discussion. We planned long lunch breaks, in order to permit a relaxed atmosphere and never run after the speakers to conclude

his/her talk in the allocated time. All participants played this game very well, so that at the end

the talk/discussion ratio was smaller than 50%.

The poster session, which served as support for fruitful discussion was open all along the workshop.


Francesco Sottile (Ecole Polytechnique, Palaiseau, France)
Pina Romaniello (University Paul Sabatier, France)
Arjan Berger (University Paul Sabatier, France)

Detailed description of the sessions and talks:

Day 1 started with the talk of Valerio Olevano, setting the ground for theoretical benchmarks of many-body theories with the respect to the exact solution of Helium atom. The second session of the day put the accent on the description of satellites for the photoemission spectra. The latter is contained in the one-particle Green’s function, well beyond the quasi-particle approach. Lucia Reining and Xavier Gonze illustrated the importance of screening effects for plasmon and phonon satellites.

Day 2 was devoted to the GW approximation (and beyond) from all points of view: theoretical developments, connection to Density functional and Density Matrix, applications and numerical implementations benchmarks: Fabien Bruneval and Jack Wetherell made useful connections between GW and density and density matrix functional theory; Michiel van Setten gave an overview on the efficiency and accuracy or today implementations of GW, along different basis sets, codes and approaches; Claudia Rödl (day 3) and Xavier Blase presented results for frontiers applications, involving disordered organic materials and transparent semiconductors; Pierre-François Loos brought a quantum chemist point of view on the problems of self-consistency for GW and beyond; finally Patrick Rinke gave insights for the description of core excitations within GW, as well as an overlook of artificial intelligence applied to solid state theory.

Developments for non-linear and non-equilibrium approaches were the objectives of Day 3. In the morning Christian Vorwerk illustrated an all-electron Green’s function approach to Resonant Inelastic X-ray Scattering, while Claudio Attaccalite presented a way to tackle phonon-assisted luminescence. In the afternoon non-equilibrium Green’s functions methods were tackled, by Davide Sangalli and Gianluca Stefanucci: both applications and theoretical aspects were discussed, including transport, electron and exciton dynamics, exciton condensation, etc.

In Day 4 the discussions turned towards more correlated materials and related approaches, with the contributions of Klaas Giesbertz, Karen Hallberg and Karsten Held. The strong correlation concept was an opportunity to discuss about the advantages of the reduced density matrix approaches (Klaas), the potential contribution of Density Matrix Renormalization Group to the description of spectral function (Karen), or the extension of the Bethe-Salpeter diagrams to Parquet Theory for the description of new excitations like π-tons (Karsten).


Day 1 – Tuesday 14 May, 2019

14:15 – 15:00 Registration

15:00 – 15:50 Presentation – Valerio Olevano (Helium atom Hylleraas exact solution as benchmark for many-body theories)

15:50 – 16:20 Coffee break

16:20 – 17:10 Presentation – Lucia Reining (Effects of dynamical screening in one-and two-body Green’s functions)

17:10 – 18:00 Presentation – Xavier Gonze (Quasiparticles and phonon satellites in spectral functions: zero-point motion, Fröhlich polaron and cumulants)

Day 2 – Wednesday 15 May, 2019

9:30 – 10:20 Presentation – Fabien Bruneval (The linearized GW density matrix)

10:20 – 10:50 Coffee break

10:50 – 11:40 Presentation – Michiel van Setten (Accuracy and precision in GW calculations)

11:40 – 12:30 Presentation – Pierre-François Loos (Green functions and self-consistency: an unhappy marriage?

12:30 – 14:30 Lunch

14:30 – 15:20 Presentation – Jack Wetherell (Correcting the GW self-screening error with a spatially local density functional)

15:20 – 16:10 Presentation – Patrick Rinke (GW and beyond: core excitations, strong correlation and artificial intelligence)

16:10 – 16:40 Coffee break

16:40 – 17:30 Presentation – Xavier Blase (Embedded many-body GW and Bethe-Salpeter formalisms for disordered organic systems)

17:30 : Poster session

20:00 : Social dinner

Day 3 – Thursday 16 May, 2019

9:30 – 10:20 Presentation – Christian Vorwerk (All-electron Many-Body Approach to Resonant Inelastic X-ray Scattering)

10:20 – 10:50 Coffee break

10:50 – 11:40 Presentation – Claudio Attaccalite (Theory of phonon-assisted luminescence: application to the hexagonal boron-nitride)

11:40 – 12:30 Presentation – Claudia Rödl (Predicting and Engineering the Optical Properties of Semiconductors: From Laser Sources to Transparent Conductors)

12:30 – 14:30 Lunch

14:30 – 15:20 Presentation – Davide Sangalli (Coherent and non coherent excitons dynamics)

15:20 – 16:10 Presentation – Gianluca Stefanucci (First-principles NEGF approach to ultrafast electron dynamics)

16:10 – 16:40 Coffee break

16:40-19:00 Poster session

Day 4 –Friday 17 May, 2019

9:30 – 10:20 Presentation – Klaas Giesbertz (Approximate energy functionals for one-body reduced density matrix functional theory from many-body perturbation theory)

10:20 – 10:50 Coffee break

10:50 – 11:40 Presentation – Karen Hallberg (Calculating precise spectral densities in correlated systems)

11:40 – 12:30 Presentation – Karsten Held (π-tons — the generic optical excitations of correlated systems)

Event website (with participant, program and presentations)

General Remarks:

From the organizers’ (and participants – see feedback below) point of view the workshop was a frank success. The level and amount of discussion was always very high, and we have been glad to notice how the discussion time has always been stretched much over the allocated time (that was also the reasons for long coffee and lunch breaks).

All participants attended the social dinner on Wednesday.

Finally, we want to thank the logistic and the people at Cecam, especially for the anomalous conditions that afflicted Cecam and obliged all of us to work with emails and telephone calls.

Without the extra effort (and very prompt answers) of Joanna, Guy, Bogdan and Nathalie the organization of the workshop wouldn’t have been possible.

Feedback from the participants:

Without any particular claim of scientific study and accurate statistics, we performed an analysis on anonymous feedback (thanks to all for actively contributing to the feedback).

The overwhelming majority liked and considered ideal: the topics, the speakers, the organization and the format. Some useful suggestions came for what concerns the hotel location, the young researchers participation and … the amount of beverage during the poster session. The pdf with full result follows:


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