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Many materials with d-shell electrons exhibit new phases of matter with striking properties. Amongst those new phases of matter, high-temperature 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 mean-field 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 three-dimensional materials. It is apparent however that in highly anisotropic materials, such as the quasi-two-dimensional high-temperature superconductors, this approach is insufficient. A number of cluster generalizations of DMFT-like 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 self-energy 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 mini-workshop 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.

Our sponsors

Our organizers

George Sawatzky

Andre-Marie Tremblay
Does the Hubbard model have a d-wave superconducting ground state?
What is the origin of the pseudogap in high-temperature superconductors?
When do stripes and other inhomogeneous phases appear?
The Mott transition beyond DMFT:
What is the effect of spatial correlations on the Mott transition?
Can optical lattices mimic correlated materials?
What is the importance of electron-phonon interactions?
How can we treat frustrated spin systems?
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