PhD defense Renaud GARIOUD

Renaud Garioud will publicly defend his thesis work on Tuesday 4th July. The defense will be held at 3p.m. in room 2 of Collège de France (Collège de France, 11 Pl. Marcelin Berthelot, 75231 Paris)

Title: When perturbation theory becomes non-perturbative : application to strongly correlated systems

Advisor: Michel Ferrero

Abstract : Strongly correlated materials reveal remarkable physical phenomena at low temperatures. Depending on external parameters, they exhibit extremely different electronic phases, ranging from insulating magnetic orders to strong superconductivity with infinite electrical conductivity. The richness of these physical phenomena takes its roots in the strong interactions that impact heavily the behaviour of electrons. To accurately describe these properties, one must solve the quantum many-body problem of interacting particles. In this thesis, we focus on the development of new algorithms to address strongly interacting fermionic systems.

By considering electronic interactions as a perturbation to the non-interacting system, we focus on computing efficiently, and up to high orders, the perturbation series, which can be expressed as sums of Feynman diagrams. We present the CDet (Connected Determinants) state-of-the-art algorithm which allows us to reach high perturbation orders. We overcome one of the main limitations of perturbation theory by introducing a novel chemical potential shift that breaks a symmetry. We show that this approach allows us to describe perturbatively the physics of ordered phases in the thermodynamic limit. We apply this new algorithm to the cubic half-filled Hubbard model and provide a quantitative description of the Néel order both near the phase transition and at low temperature up to the high coupling regime. This study enables us to detail the limitations to our method and to present the numerical tools that ensure an efficient implementation of the CDet algorithm and an accurate resummation of the resulting perturbative series. The attractive counterpart of this model shows a superconducting phase that can also be described by adapting our symmetry-breaking approach.