# Soutenance de thèse

**Alice Moutenet (groupe Matière condensée)**

Soutiendra publiquement ses travaux de thèse intitulés

**"Novel algorithms for strongly correlated quantum systems in and out of equilibrium"**

dirigés par Monsieur Antoine GEORGES et Monsieur Michel FERRERO

Soutenance prévue le vendredi 03 juillet 2020 à 14h30

Lieu : Collège de France 11, place Marcelin Berthelot 75005 Paris

Salle : viso conférence + Salle 2

__Abstract__

What do stars in a galaxy, drops in a river, and electrons in a superconducting cuprate levitating above a magnet all have in common? All of these systems cannot be described by the isolated motion of one of their parts. These singular properties emerge from particles and their interactions as a whole: we talk about the many-body problem.

In this Thesis, we focus on properties of strongly-correlated systems, that obey quantum mechanics. Analytical methods being rapidly limited in their understanding of these materials, we develop novel numerical techniques to precisely quantify their properties when interactions between particles become strong.

First, we focus on the equilibrium properties of the layered perovskite Sr2IrO4, a compound isostructural to the superconducting cuprate La2CuO4, where we prove the existence of a pseudogap and describe the electronic structure of this material upon doping.

Then, in order to address the thermodynamic limit of lattice problems, we develop extensions of determinant Monte Carlo algorithms to compute dynamical quantities such as the self-energy. We show how a factorial number of diagrams can be regrouped in a sum of determinants, hence drastically reducing the fermionic sign problem.

In the second part, we turn to the description of nonequilibrium phenomena in correlated systems. We start by revisiting the real-time diagrammatic Monte Carlo recent advances in a new basis where all vacuum diagrams directly vanish. In an importance sampling procedure, such an algorithm can directly address the long-time limit needed in the study of steady states in out-of-equilibrium systems.

Finally, we study the insulator-to-metal transition induced by an electric field in Ca2RuO4, which coexists with a structural transition. An algorithm based on the non-crossing approximation allows us to compute the current as a function of crystal-field splitting in this material.

__Jury__

M. Antoine GEORGES, Collège de France, Directeur de thèse

M. Michel FERRERO, École polytechnique, Co-directeur de thèse

Mme Laura MESSIO, Sorbonne Université, Examinateur

M. Marco SCHIRO, CEA-Saclay, Examinateur

M. Philipp WERNER, Université de Fribourg, Rapporteur

M. Sylvain CAPPONI, Université Paul Sabatier de Toulouse, Rapporteur