Modeling many-body physics with Slave-Spin Mean-Field: Mott and Hund's physics in Fe-superconductors

Slave-spin mean-field theory, a light and accurate technique to model electronic correlations in Fermi-liquid phases of multi-orbital materials, is pedagogically exposed in this chapter, with a focus on its recent successful application to the physics of Iron-based superconductors. Beside introducing electronic correlations and recalling the Fermi-liquid phenomenology, the manuscript accompanies the step-by-step explanation of the slave-spin technique with a set of useful complements providing analytical insight into Mott and Hund's physics, which are at the heart of the physics of strongly correlated materials. Some original research material is also exposed, such as the Hund-induced shrinking of the Hubbard bands flanking the gap of the half-filled Mott insulator, and the low-energy description of the "orbital-decoupling" mechanism.