We present an improved upper bound for the ground-state energy of lattice fermion models with a sign problem. The bound can be computed by numerical simulation of a recently proposed family of deformed Hamiltonians with no sign problem. For one-dimensional models, we expect the bound to be particularly effective and practical extrapolation procedures are discussed. In particular, in a model of spinless interacting fermions and in the Hubbard model at various filling and Coulomb repulsion we show how such techniques can estimate the ground-state energies and correlation function with great accuracy.
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. 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 cannot be slower than the inverse square law at low temperatures and the inverse law at high temperatures, while the on-site pairing correlation function cannot 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.