Variational Monte-Carlo Studies of Hubbard Model. I

A variational Monte-Carlo method, which is a combination of the variational theory and the Monte-Carlo technique is proposed to study the Hubbard model with the Gutzwiller's wave function. An application is made to one-, two-, and three-dimensional models having sites up to 216 (6×6×6) and arbitrary values of U / t (on-site repulsion U and hopping integral t ). Contrary to resorting to the Gutzwiller approximation, it provides a virtually exact way to carry out the Gutzwiller-type variational theory and opens up a possibility of further development.