Ab initio description of strongly-correlated materials: On the road to predictive power

Strongly-correlated materials show a variety of fascinating
properties, such as metal-insulator transitions, unconventional
superconductivity, or strongly enhanced magnetism. A common feature of these fascinating materials is that potential and kinetic energy are of similar strength and compete with each other, yielding fragile and easy-to-perturbe ground states.

The theoretical description of these correlated compounds is challenging, since both the itinerant motion of electrons and local atomic-like physics has to be taken into account on the same footing. This goal can be reached by combining density functional theory with the dynamical mean-field theory [1], which allows for a continuous interpolation between itinerant metals on the one hand, and strongly-localized insulators on the other hand.

In this talk I will review recent advances in this field, using selected topical examples. We will see how new developments of numerical methods made it possible to address questions that we could not answer a few years ago [2,3]. I will for instance discuss correlation effects in iron-based superconductors, and highlight the effect of Hund's rule coupling in these materials. We will furthermore identify this coupling to be the reason for quite a number of unexpected properties in 3d in 4d materials [4-6].

Although these examples will show that we have seen tremendous progress in the ab initio description of correlated matter in recent years, we are still not at the end of the road to true predictive power. I will discuss the open issues in the context of one of our current research focuses, which are spin-orbit coupled correlated systems, such as iridium oxide crystals [7] and heterostructures.

[1] G. Kotliar et al., Rev. Mod. Phys. 78, 865, (2006).
[2] M. Aichhorn et al., Phys. Rev. B 80, 085101 (2009).
[3] M. Aichhorn et al., Comp. Phys. Comm. 204, 200 (2016).
[4] M. Aichhorn et al., Phys. Rev. B 82, 064504 (2010)
[5] J. Mravlje et al., Phys. Rev. Lett. 108, 197202 (2012).
[6] M. Zingl et al., Phys. Rev. B 94, 045130 (2016).
[7] C. Martins et al., Phys. Rev. Lett. 107, 266404 (2012).