# Dresden 2020 – wissenschaftliches Programm

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# TT: Fachverband Tiefe Temperaturen

## TT 33: Correlated Electrons: Method Development 1

### TT 33.2: Vortrag

### Mittwoch, 18. März 2020, 09:45–10:00, HSZ 201

TRILEX^{2} approach: towards the calculation of realistic systems — •Evgeny A. Stepanov^{1}, Silke Biermann^{2}, and Alexander I. Lichtenstein^{1} — ^{1}Institute of Theoretical Physics, University of Hamburg, Germany — ^{2}Centre de Physique Theorique, Ecole Polytechnique, Palaiseau, France

A theoretical description of strongly correlated realistic systems is a challenging issue. A state-of-art method that allows to obtain single-particle properties of a corresponding multi-band electronic problem is the dynamical mean field theory (DMFT). Starting from DMFT, it is known that a consistent calculation of two-particle susceptibilities can be done via a ladder diagram that necessarily contains local vertex corrections. However, a calculation of these vertices is the most complicated and time consuming part of numerical approaches that describe nonlocal collective effects diagrammatically beyond DMFT. In some cases, a description of collective electronic fluctuations can be performed in a much simpler way using the GW+DMFT theory. However, the GW+DMFT in its original form accounts for the screening of the local Coulomb interaction only in the charge channel. Thus, the effect of the magnetic fluctuations in the nonlocal self-energy is missing. Recently, some of us introduced a computationally inexpensive TRILEX^{2} approach [PRB 100, 205115 (2019)] that describes nonlocal many-body effects in the GW+DMFT style, but allows for a simultaneous account for collective excitations in different (charge, spin, etc.) bosonic channels. Here, we apply this method to a multi-band Hubbard model to explore orbital and spin fluctuations.