Theoretical research will be conducted on high temperature superconductors (copper oxides). This work is motivated by the close proximity, at low doping concentrations of oxygen, of the superconducting phase to the antiferromagnetic phase. Our recently developed semiclassical expansion of a model in this regime allows for a controlled study of the slightly doped antiferromagnet. The comparison for these single hole results to numerical simulations and experiments is encouraging. The many hole problem has not been studied and the proposed projects will clarify the effects of finite doping on the magnetic order and on the evolution from an antiferromagnetic insulator to a high temperature superconductor. %%% This project will theoretically study one model for high temperature superconductors and its behavior before becoming superconducting. Thus, the effect of oxygen doping on the magnetic properties prior to becoming superconducting and the influence of doping on superconductivity will be studied. This problem is one of the foremost ones in condensed matter physics and materials science.
