Generalizations of Dynamical-Mean Field Theory and Improved Solvers
“Generalizations of Dynamical-Mean Field Theory and Improved Solvers ½”
“Generalizations of Dynamical-Mean Field Theory and Improved Solvers 2/2”
Dynamical Mean-Field Theory (DMFT), developed in good part in Paris, is the basis for many of the successes presented in this series of lectures. Here I first recall physical intuitions and concepts that are behind DMFT and generalizations that are necessary to work in low dimensions. I present advantages and disadvantages of various versions of the approach, from Cluster Perturbation Theory to Variational Cluster Approximation, Cellular Dynamical Mean Field Theory and Dynamical Cluster Approximation. I briefly discuss various versions of so-called “impurity solvers”, from exact diagonalization to Continuous-Time Quantum Monte Carlo. In the second part of the talk, I proceed more formally, introducing the Luttinger-Ward Functional and showing how various schemes follow from this. I expand on a few details of solvers, briefly discuss the problem of analytical continuation and end with open questions.