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Toward material-specific simulations of high temperature superconductivity

High temperature superconductors could potentially revolutionize the use and transmission of electric power. This along with intriguing scientific questions have motivated an enormous research effort over the past twenty years, since the discovery of high temperature superconducting cuprates. But only recently, with the advent of massively parallel vector supercomputers and quantum cluster methods to solve the quantum many-body problem, has it become possible to simulate superconductivity in models such as the 2D Hubbard model that are thought to describe the cuprate superconductors. In this presentation, we will discuss the recent progress we have made in understanding superconductivity in the Hubbard model, as well as what seem to be the key ingredients for the development of materials specific extensions that will eventually allow predictive simulations of the superconducting transition temperature. We will also discuss the computational challenges we face with materials specific simulations of superconductivity.