


Many materials with dshell electrons exhibit new phases of matter with
striking properties. Amongst those new phases of matter, hightemperature
superconductivity is an important example. Yet the numerous analytical
tools developed to date are not sufficient to provide quantitative
predictions form microscopic models of these compounds. In recent years,
new numerical methods such as dynamical meanfield theory (DMFT), and new
and more powerful computer architectures (clusters), have provided a way
to make progress. DMFT can give quantitative predictions that are in
principle exact in infinite dimension and a good approximation in
threedimensional materials. It is apparent however that in highly
anisotropic materials, such as the quasitwodimensional hightemperature
superconductors, this approach is insufficient. A number of cluster
generalizations of DMFTlike methods offer hope to tackle these problems.
Several of these "Quantum Cluster" methods are now available: Dynamic
Cluster Approximation, Cellular Dynamical Mean Field theory, Cluster
Perturbation Theory and Variational Cluster Perturbation Theory. The
selfenergy functional approach has even given a conceptual framework to
highlight links between these different approaches. Other approaches, such
as variational wave functions, exact diagonalizations, Quantum Monte Carlo
methods, Density Matrix Renormalization Group and Stochastic Series
expansion also have much to offer.
The main purpose of this miniworkshop will be to confront the different numerical approaches to find which features of materials can be reproduced by all approaches and, when the methods differ in their predictions, to find which approach should be preferred. It seems in fact that there is enough concordance between the various approaches to answer in a credible manner timely and important physical questions on which the workshop will focus. 

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