What is the Hamiltonian for high-temperature superconductors?
While the Hamiltonian of any periodic solid is known, the large number of particles and the huge differences in energy scales that are contained in this Hamiltonian make it impossible to predict from first principles phenomena such as high temperature superconductivity. As in many other branches of Physics, one must begin with an effective Hamiltonian. Yet, even the simplest effective Hamiltonian remains a challenge to solve reliably. This means that often one does not know whether agreement with experiment is fortuitous or reflects accurately the Physics contained in the effective Hamiltonian. It is thus important to improve the accuracy of approximate methods, to devise new approaches, and to obtain agreement between these different approaches. Methods that use exact solutions of small clusters offer a new promising way to attack the problem of high-temperature superconductivity. I will discuss a new unified variational point of view recently proposed by Potthoff that contains as spe
