The aim of the course is to become familiar with methods and concepts of strongly correlated electrons and superconductors through a practical implementation of some of the methods presented in the basic course to models of current interest motivated by quantum materials and quantum simulators with cold atoms. 

According to the number of participants, I will form one of more working groups each with an assigned problem

Candidate topics include (but are not limited to)

1) Two-band superconductors. I will introduce the main changes of the theory of superconductivity when more than one band is relevant, a situation which is relevant to a class of iron-based superconductors, and I will propose a problem about the competing phases of a model with on-site attractive interactions, playing with linear-response theory and mean-field theory.

2) Two-orbital insulators. I will introuduce the physics of multiorbital Hubbard model and propose a problem about the phase diagram of a two-orbital model as a function of the different interaction parameters (Hubbard U and local exchange J) playing with linear-response theory and mean-field theory. A sub-option is to consider models for topological insulators.