An introduction to quantum cluster methods

Abstract

These lecture notes provide an introduction to quantum cluster methods for strongly correlated systems. Cluster Perturbation Theory (CPT), the Variational Cluster Approximation (VCA) and Cellular Dynamical Mean Field Theory (CDMFT) are described, as well as the exact diagonalization solver for the cluster. Potthoff's self-energy functional formalism is reviewed. Some numerical procedures, in particular regarding the exact diagonalization method and the frequency-momentum integrals needed in VCA, are discussed in detail.

25 pages, 22 figures. Lectures given at the CIFAR - PITP International Summer School on Numerical Methods for Correlated Systems in Condensed Matter, Sherbrooke, Canada, May 26 -- June 6 2008 (this version fixes typos and updates some notation)

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