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## Green's function methods: the next generation 6

#### Location: CECAM-FR-GSO, Toulouse, France

#### Organisers

Green's functions have always played a prominent role in many-body physics. In particular one and two-body Green's function deliver a wealth of information about a physical system, such as ground-state energies, ionization potentials, electron affinities, spectral functions, excitation energies, absorption spectra, etc. Therefore the development of approximate methods to calculate the one-body Green's function 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 Green's functions. A very popular class of methods is based on the solution of an integral equation for the one-body Green's function 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 photoemission 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 Green's functions. A new wave of original ideas, understanding, and solutions, has pervaded the field in these last years. Many new developments have occurred since the last successful "Green's function methods" workshop we held in Toulouse in November 2022. In particular the community has seen:

- new strategies to improve GW calculations: using the space-time approach [1], doing fully self-consistent GW for solids at finite temperature [2], improved total energies [3] and core-level binding energies in molecules [4] and the stochastic integration of the screened interaction for low-dimensional systems [5]
- novel approaches to go beyond the GW method: including higher order terms in the perturbation expansion [6], using coupled-cluster Green functions [7,8] and using diagrammatic Monte Carlo [9]
- new methods to treat electron-electron and electron-phonon correlations on an equal footing [10,11]
- advances in neighbouring fields such as DFT [12,13] and DMFT [14] and 2RDM [15]
- new insights: the importance of the inclusion of the continuum states [16], the advantages of symmery-breaking [17], RIXS spectra from BSE calculations [18], and the prediction of excitonic insulators [19] and the radiative lifetimes of excitons [20].

Therefore it is timely to gather these novel explorations in a sixth edition of this workshop. In particular we would like to answer the following questions.

- How important are self-consistency and vertex corrections and how are there systematic cancelations between the two?
- For which observables and/or materials do we have to go beyond
*GW*and what are the best strategies to do so? - What can the
*ab-intio*condensed-matter community learn from other communities, such as the quantum chemistry, the DFT, the DMFT, and the 2RDM communities. - What are the best strategies to go beyond perturbation theory (in the density, the screening, the potential)?

## References

**France**

Arjan Berger (Toulouse University) - Organiser

Pina Romaniello (Université de Toulouse) - Organiser

Francesco Sottile (Ecole Polytechnique) - Organiser