Laboratoire de Physique Théorique
Toulouse - UMR 5152

Finding a way to numerically simulate many interacting quantum particles would be of great fundamental and practical value. In this talk, I will discuss a broad class of approaches based on diagrammatic expansions that allows to obtain numerically-exact results in a time polynomially increasing with the inverse of the requested precision. Recent advances allow to include renormalization and non-perturbative information (e.g. Dynamical Mean Field Theory for lattice problems) in the expansion using a succinct, and, most importantly, very efficient, formalism. I will present state-of-the-art numerically-exact results for the doped square-lattice Hubbard model, and the generic efficient code we have developed.