Quantum cluster methods for strongly correlated materials

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Our understanding of materials has long been based on simple paradigms: metals can be understood in terms of quasi-independent electrons, undergoing occasional collisions; at the other extreme, magnets are understood in terms of the spins of localized electrons. But between these paradigms lies a spectrum of materials that defy comprehension in terms of these simple pictures, even though they may show characteristics of both. High-temperature superconductors, discovered nearly 30 years ago, are the prototype of such "strongly correlated materials". Such materials display a variety of fascinating properties, from superconductivity to exotic magnetism, charge order, etc. They have tremendous potential. Technological advances based on these properties will be guided by a deeper understanding of strongly correlated materials.