High-temperature superconductivity in cuprates and organics : where do we stand ? (8)

Dynamic Mean Field Theory (DMFT), developed largely in Paris, is the basis for many of the important results presented in this series of lessons. Here I first recall the physical intuition and concepts behind DMFT, and the generalizations that are necessary for working in low dimensions. I present the advantages and disadvantages of several versions of this approach, from perturbation theory on clusters, through the variational cluster approximation, dynamic mean-field theory on clusters and the dynamical cluster approximation. I briefly discuss different versions of so-called "impurity solvers", from exact diagonalization to continuous-time Quantum Monte Carlo. In the second part of this presentation, I introduce the Luttinger-Ward functional more formally and demonstrate how several of the approaches mentioned above can be derived from it. I explain some details of the solvers, briefly discuss the analytical extension problem and conclude with some open questions.