Path Integral Studies of the 2D Hubbard Model Using a New Projection Operator

Feynman’s path integral formulation of quantum mechanics, supplemented by an approximate projection operator (exact in the case of noninteracting particles), is used to study the 2D Hubbard model. The projection operator is designed to study Hamiltonians defined on a finite basis set, but extensions to continuous basis sets are suggested. The projection operator is shown to reduce the variance by a significant amount relative to straightforward Monte Carlo integration. Approximate calculations are usually within one standard deviation of exact results and virtually always within two to three standard deviations. In addition, the algorithm scales with the number of discretization points P as either P or P 2 (depending on the method of implementation), rather than the P 3 of the Hubbard–Stratonovich transformation. Accuracy to about 5%–10% in energies and spin–spin correlation functions are found using moderate amounts of computer time