Two-particle self-consistency in diagrammatic theories for strongly correlated electron systems

• Applicant: Dr. Georg Rohringer
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2018 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 407372336

Strongly correlated materials exhibit some of the most exciting phenomena in solid state physics, including high-temperature superconductivity, magnetism or giant magneto-resistance. In view of these fascinating physical properties, which are potentially also of high technological relevance, a comprehensive theoretical understanding of such systems is highly desirable. In this respect, substantial progress has been achieved in the last 20 years by dynamical mean field theory (DMFT) which captures a relevant part of the correlations, i.e. the local ones. However, most of the remarkable physics of correlated electrons on a lattice is also strongly influenced by non-local correlations effects. To include them in the theoretical description, a number of so-called “diagrammatic extensions” of DMFT has been developed in the last decade. These quantum field theoretical approaches perform a (Feynman) diagrammatic expansion around DMFT which includes non-local correlation effects on top of the local ones of DMFT. However, in spite of the intense forefront research on these techniques in the last years they still exhibit serious limitations. First of all, they are not fully two-particle self-consistent which means that they might yield different results for physical observables (such as the potential energy) when they are calculated in different ways (i.e. from one- or two-particle correlation functions). Moreover, in their current implementations they are applicable only to simple one-band model Hamiltonians but not for the description of realistic correlated materials. In this project, we will develop a new method on the basis of existing schemes, such as, e.g. the dynamical vertex approximation, which will overcome these limitations in an efficient way. This will be achieved by physically driven renormalization of the two-particle correlation functions (susceptibilities) which are obtained by the respective diagrammatic extensions of DMFT. This approach will be then extended from a single- to a multi-orbital treatment in order to make it applicable for the investigation of realistic correlated materials. The new algorithms developed within the project will be then exploited to obtain fundamentally new insights into the physics of strongly correlated electron systems. Specifically, we will investigate antiferromagnetism and its interplay with unconventional superconductivity in model as well as realistic systems such as cuprates, itinerant magnetism in iron and nickel, and the Hall conductivity in the Hubbard model in an external magnetic field. The latter will allow for exciting new insights into the effects of strong non-local correlations on topological states of matter. Eventually, our theoretical improvements will lead to an unambiguous and thermodynamically consistent description of many-electron properties, a highly relevant topic also for reliable lattice optimization calculations within the ab initio treatment of correlated materials.

• DFG Programme: Independent Junior Research Groups
• International Connection: Austria, Russia, USA
• Cooperation Partners: Professor Dr. Emanuel Gull; Professor Dr. Karsten Held; Professor Dr. Andrey Katanin, until 3/2022; Professor Dr. Alessandro Toschi