Jean-Marc Robin

Machine-Ecole raconte l'histoire d'un ministre de l' ducation, devenu Pr sident de la R publique, qui va mettre en place son grand projet: une cole machine qui s'appuie sur les neurosciences, la neurop dagogie et les progr s de l'informatique, d sormais capables de cr er des l ves augment s. Machine-Ecole, c'est encore l'histoire de deux France qui se combattent: une France Populaire et une France plus bourgeoise qui ne partagent pas la m me vision de la soci t et de l'individu. Machine-Ecole, c'est enfin le r cit du pouvoir grandissant des grandes firmes num riques, bien d cid es faire l'histoire.

This book is a short introduction to the Dynamical Mean-Field Theory for strongly correlated electrons. Its purpose is to focus on various local decoupling schemes in order to derive a self-consistent approximation and to map the lattice problem onto an impurity problem. Hubbard, Holstein, and Falicov-Kimball models are mainly used to provide examples of calculation. Numerous basic c/c++ programs are given along the book to develop confidence in computing actual numerical results.

We show how to set up a Cellular Dynamical Mean Field Theory for the Holstein's polaron problem using the exact solution of a cluster of n sites embedded in a Weiss's field. We show that a restricted basis, that allows excitations of phonons only for n sites at a time, reproduces exactly the equations of the n-site Dynamical Mean Field Theory, and enables to check the proposed decoupling scheme of the Green's functions via Exact Numerical Diagonalizations. We introduce a real space formulation of the Cellular Dynamical Mean Field Theory that applies to any lattice with or without periodic boundary conditions and that allows to partition the lattice into different kinds of clusters.

We review the Dynamical Mean Field Theory of the Holstein Polaron Problem in order to compute the small polaron Green's functions. The Renormalized Perturbation Expansion (RPE) play a central role and allows to compute all the local and non local Green's functions for the electron and the small polaron, for finite or infinite size systems, with periodic or non periodic boundary conditions. We introduce a restricted basis for the phonons to study the decoupling scheme of the Green's functions in a Local Approximation via exact diagonalizations. As a bonus, we furnish all the C/C++ programs built step by step, from a pedagogical point of view.