Nonlocal correlation effects in magnets and high-temperature superconductors

Strongly correlated electron systems feature a wide range of fascinating phenomena such as correlation-driven Mott metal-to-insulator transitions, different types of magnetic orders ranging from ferro- to antiferro-magnetism, high-temperature superconductivity, nematic order and many more. On the other hand, it is very challenging to describe such systems theoretically as standard mean field approaches and density-functional-theory-based methods do not provide reliable results. In this respect, the dynamical mean field theory (DMFT) has presented a huge step forward as it can capture an importation portion of the correlation effects, namely the purely local ones. To understand phenomena such as magnetism or superconductivity a comprehensive inclusion of nonlocal correlation effects is inevitable. This can be achieved by diagrammatic extensions of the DMFT which construct a Feynman diagrammatic perturbation series around the DMFT starting point (see Rev. Mod. Phys. 90, 015003, 2018). However, such methods are either numerically highly demanding and, hence, applicable only to very simple model systems such as the Hubbard model, or they suffer from intrinsic inconsistencies which lead to ambiguous results for important thermodynamic quantities such as the potential and kinetic energies.

Recently, successful attempts have been made to overcome these problems by introducing effective renormalization parameters in charge- and spin-susceptibilities which are determined by the requirement to obtain consistent results for thermodynamic observables. So far, these approaches have been developed (and applied) only for the simple one-band Hubbard-type models (see Phys. Rev. B 106, 205101, 2022).

In this project, such approaches should be generalized to realistic multiorbital systems aiming at a comprehensive description of realistic correlated materials. After the relevant equations have been derived and numerically implemented the new approach should be applied to the analysis of high-temperature superconductors such as cuprates, pnictides or nicelates. Moreover, the extension to a larger number of orbitals will open the path to an understanding of the effect of nonlocal correlations in topological states of matter where a comprehensive treatment of a moderate to large number of orbitals is indispensable.