The physical properties of most materials are dictated by the behavior of their electronic degrees of freedom. In systems deemed correlated, the interactions between electrons result in them no longer behaving independently of one another, giving rise to collective excitations, which involve the cooperation of many electrons. Such collective behavior can result in drastic changes in the material, such as a phase transition, where electrons can spontaneously reorder and behave in ways which are completely different to their parent phase. In this thesis, we apply various many-body methods based on the Dynamical Mean-Field Theory (DMFT), to study the electronic structure and ordering tendencies of such correlated electron systems. Aside from making predictions, it is equally important to be able to critically assess how these predictions compare to experiment.
This talk will focus on two selected applications of the DMFT formalism to investigate the transport and ordering tendencies of a given material or model with strong electron correlations. In particular, we investigate the resistivity of the recently studied Kagome compound Ni3In, which exhibits non-Fermi-liquid (NFL) behavior at low temperatures, and features a quasi-flat band around the Fermi level. We proceed to solve the impurity problem in the compact molecular orbital basis, and extract the temperature-dependent resistivity within the DMFT bubble approximation. The obtained results enable us to estimate the NFL-FL crossover temperature, which was observed to increase with hole doping of the parent compound. In another study, we supplement the DMFT equations with the Bethe-Salpeter formalism to study the spin susceptibility of the square lattice Hubbard model at various dopings. We obtain a temperature-doping phase diagram, uncovering regions of spin-stripe formation (spatial modulations of spin density) inside and outside of the AFM phase. The study of stripes in the Hubbard model can shed light on the superconducting mechanisms occurring in high-temperature superconductors.
The talk will start with a pedagogical introduction to correlated electron systems and the DMFT formalism for the general audience.