24.05.23: Talk by Dr. Georg Rohringer "Green's functions for the theoretical description of strongly correlated electrons systems"

Arbeitsgruppenleiter Quantenfeldtheorie für korrelierte Vielteilchensysteme Universität Hamburg Fakultät für Mathematik, Informatik und Naturwissenschaften

24.05.2023 at 09:00 

Green's functions represent one of the most useful tools for the theoretical description of correlated lattice electrons. In particular, the one-particle Green's function contains information about the spectral properties of the system and can be directly compared to (angular resolved) photoemission spectroscopy experiments. However, also two-particle correlation functions provide very interesting insights into the properties of correlated electron systems as they contain crucial information on response functions such as the magnetic susceptibility or the optical conductivity. In my talk, I will present an overview about the physical content as well as the applications of one- and two-particle Green's and vertex functions in frontier condensed matter research. First, I will demonstrate how the inclusion of local correlation effects into the one-particle Green's function by means of dynamical mean field theory (DMFT) can lead to a breakdown of the topological quantization of the Hall conductivity in the Hubbard model in a magnetic field. The limitations of the purely local description of DMFT leads me to the discussion of how local frequency-dependent vertices can be used to include non-local correlations effects in interacting many-electron systems beyond DMFT. While these so-called diagrammatic extensions[1] of DMFT have been successfully exploited to describe collective phenomena such as magnetism and superconductivity[2], their predictive power is still limited by specific inconsistencies between the one- and the two-particle level, in particular when simplified ladder calculations in one scattering channel are exploited. In the final part of my talk, I will present possible solutions to this problem[3]. [1] G. Rohringer et al., Rev. Mod. Phys. 90, 025003 (2018). [2] G. Astretsov et al., Phys. Rev. B 101, 075109 (2020). [3] J. Stobbe and G. Rohringer, Phys. Rev. B,106, 205101 (2022).