Schedule

Ian Jauslin, Rutgers University: Renormalization group analysis of hierarchical graphene

Abstract:  The hierarchical graphene model is a simple toy model which is useful to understand the mechanics of renormalization group flows in super-renormalizable systems. It is based on a model of interacting electrons in graphene, for which the renormalization group analysis was carried out by Giuliani and Mastropietro. The analysis of the hierarchical graphene model is significantly simpler than graphene, but one should not expect it to produce good quantitative results about real-world graphene. Rather, the hierarchical model is useful as a teaching tool to understand the core concepts of renormalization group techniques. In this course, we will first introduce a model for electrons in graphene and set it up for a renormalization group treatment by introducing its Grassmann representation and scale decomposition. We then define the hierarchical graphene model and study it's renormalization group flow. From a renormalization group point of view, graphene is quite simple: it is super-renormalizable. As an illustration of a more complicated system, we repeat the analysis for the Kondo model, which is a strongly coupled model with a non-trivial fixed point.

Phan Thành Nam, LMU (Münich): Bosonization and Bogoliubov diagonalization method for Fermi gases

Abstract: We will discuss a rigorous bosonization method to compute the correlation energy and the elementary excitations of weakly interacting Fermi gases from first principles. In this approach, the main energy contribution beyond the Hartree-Fock theory is described by a quadratic Hamiltonian in terms of quasi-bosonic operators, which can be diagonalized by a quasi-bosonic Bogoliubov transformation. This argument was already proposed on a heuristic level by Sawada-Brueckner-Fukuda-Brout in 1957, in relation to the random phase approximation of Bohm and Pines,  but the rigorous implementation is highly nontrivial since the bosonic property only emerges in a very weak sense. The lecture will based on recent joint work with Martin Ravn Christiansen and Christian Hainzl, as well as earlier joint work with Niels Benedikter, Marcelo Porta, Benjamin Schlein, and Robert Seiringer.

Lecture: Ian Jauslin (Aud 4)

Excursion: Kayak tour 15:00-17:00, Kayak Republic, Børskaj 12. Dinner from 19:15-20:45 (sharp!), The Food Club, Sortdam Dossering 7C.

Coffee 

Lecture: Ian Jauslin

Goodbye