There is a widespread feeling that the discovery of high temperature superconductors will force us to change our way of thinking about superconductivity in solids. It has steadily emerged that the simple free-electron picture is inadequate, that a new mechanism of superconductivity is most likely at work, and that modifications (if not outright revisions of the many-body theory) are needed. The situation is not entirely without precedent: much the same could have been said of superfluidity in liquid He. That, however, did not cause such a stir: it had been anticipated some 12 years before its eventual discovery, and the transition temperature of liquid He is so low that experiments have been confined to the few laboratories around the world with a milli-kelvin capability. Finally, the normal state of He was already wellunderstood, so that theorists were poised and ready to tackle the problems posed by the superfluid.Contrast the oxides. Even the rather extensive earlier studies of Ba1-x PbxBiO3 and other superconducting oxides did not prepare us for the advances of the past two years. Laboratories all over the world have been able to prepare and study the new superconductors rather easily, although well-characterized samples and incisive experiments have not been so easy to come by. The flood of new information poses a particular challenge for condensed matter theory — to distil the essence of these complicated multicomponent materials and to explain how the genie of high temperature superconductivity has escaped after so many years. Despite the existing understanding of the properties of oxides, much work remains to be done before we have a good grip on the many-body theory of these strongly correlated systems.
Symmetry reduction of tensor networks in many-body theory