Magnetic and Pairing Correlations in Correlated Electron Systems

Magnetic and superconducting pairing correlation functions in a general class of Hubbard models, the t-J model and a single-band Hubbard model with additional bond-charge interaction are investigated, respectively. Some rigorous upper bounds of the corresponding correlation functions are obtained. It is found that the decay of the spin-spin correlation function with temperature in the general Hubbard models can not be slower than the squared inverse law at low temperatures and the inverse law at high temperatures, while the on-site pairing correlation function can not be slower than the inverse law. An upper bound for the average energy of the t-J model is found. The upper bounds for the spin-spin and the electron pairing correlation functions in the t-J model as well as in the Hubbard model with bond-charge interaction are also obtained. These bounds are expected to provide certain standards for approximate methods. In some special cases, these bounds rule out the possibility of corresponding magnetic and pairing long-range order.