Kilian Fraboulet (Université Paris-Saclay)

Path-integral approaches to strongly-coupled quantum many-body systems: applications to a (0+0)-D O(N) model

Friday, 11 June 2021, 2pm (online)

As many-body physicists, we aim at designing reliable and computationally affordable methods to describe many-body quantum systems. The path-integral formulation of quantum field theory provides us with plenty of techniques to achieve this. We will particularly focus on its ability to describe strongly-coupled many-body systems of finite size. In particular, collective behaviors can be efficiently described in such systems through the exploitation of spontaneous symmetry breaking (SSB) in mean field approaches. However, for mesoscopic systems, the fluctuations of order parameters associated with broken symmetries can not be neglected and tend to radiatively restore such symmetries. Hence, the efficiency of theoretical approaches in the treatment of finite-size quantum systems can notably be studied via their ability to restore spontaneously broken symmetries.

In this respect, a zero-dimensional O(N) model is taken as a theoretical laboratory to perform a comparative study of many state-of-the-art path-integral techniques combined or not with Hubbard-Stratonovich transformations: perturbation theory with various resummation methods (Padé-Borel, conformal mapping, Meijer-G), enhanced versions of perturbation theory (transseries derived via Picard-Lefschetz theory, optimized perturbation theory), self-consistent perturbation theory based on effective actions (CJT formalism, 4PPI effective action,...), functional renormalization group (FRG) techniques (FRG based on the Wetterich equation, DFT-FRG, 2PI-FRG). Some connections between these methods will be emphasized and their performances in the strongly-coupled regime will be examined in detail.