New Directions in Theoretical Studies of Iron-based Superconductors

The discovery of high T_c superconductivity in iron-based pnictides and chalcogenides brought to the forefront the need to develop efficient theoretical procedures to treat multiorbital models of interacting electrons. Among the many challenges, we need to clarify the role that the orbital degree of freedom plays in pairing and how its interaction with magnetic and lattice degrees of freedom leads to the stabilization of exotic phases such as the nematic state. Theoretical studies in the strong and weak coupling limits cannot address the physically relevant intermediate regime, with a mixture of itinerant and localized degrees of freedom. Traditional numerical methods, such as Lanczos or quantum Monte Carlo, have either a too rapidly growing Hilbert space with increasing size or sign problems. For this reason, it is necessary to develop new models and techniques, and also better focus on systems where both experiments and accurate theory can be used in combination to reach a real understanding of iron pairing tendencies. Examples of recent advances along these directions that will be discussed in this talk include: i) The development of spin-fermion models [1] that allow studies in the difficult nematic regime with a finite short-range antiferromagnetic correlation length above the ordering critical temperatures. This type of studies also allow the inclussion of doping, quenched disorder, and the study of transport and real-frequency responses; ii) The application of the Density Matrix Renormalization Group approach to multi-orbital Hubbard models in chain and ladder structures [2] triggered by the discovery of superconductivity at high pressure in ladder iron-based compounds such as BaFe₂S₃ and BaFe₂Se₃. In this context, the recently reported [2] pairing tendencies unveiled at intermediate Hubbard U will be discussed.

[1] S.Liang et al., Phys.Rev.Lett. 109, 047001 (2012) .

[2] N. Patel et al., Phys. Rev. B 96, 024520(2017).