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Report on Green’s function methods: the next generation

Objectives:

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.

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Theoretical Spectroscopy Lectures

October 8, 2018 to October 12, 2018
Location: CECAM-HQ-EPFL, Lausanne.

The aim of the school was to give a deep introduction on the theoretical and practical aspects of the electronic excitations, which are probed by experimental techniques such as optical absorption, EELS and photo-emission (direct or inverse). From the theory point of view, excitations and excited state properties are out of the reach of density-functional theory (DFT), which is a ground-state theory. In the last thirty years, other ab-initio theories and frameworks, which are able to describe electronic excitations and spectroscopy, have become more and more used: time-dependent density-functional theory (TDDFT) and many-body perturbation theory (MBPT) or Green’s function theory (GW approximation and Bethe-Salpeter equation BSE). In fact, computational solutions and codes have been developed in order to implement these theories and to provide tools to calculate excited state properties. The present school focused on these points, covering theoretical, practical, and also numerical aspects of TDDFT and MBPT, non-linear reponse and real-time spectroscopies. Finally, a large part of the school was devoted to the codes implementing such theories (ABINIT, 2Light, Lumen, DP, EXC).

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