Effective quantum variational Monte Carlo study of Hubbard model

Abstract

It is important to understand the physics of correlated itinerant electron systems characterized by the on-site Coulomb repulsion U . The two-dimensional Hubbard model is one of the simplest models for the description of such correlated systems. The Gutzwiller-projected wave function has been improved by considering effective electron correlation or long-range Jastrow-type correlation. Elaborate extra correlation operators optimize the electron correlation and lower the ground-state energy considerably. The kinetic operator effectively optimizes the Gutzwiller function: ψ λ = e - λ K P G ψ 0 , where K is the kinetic energy term of the Hubbard Hamiltonian and P G is the Gutzwiller operator. The Gutzwiller–Jastrow function is also an well optimized wave function. We have developed a quantum Monte Carlo optimization method for many fermion systems as an intensive extension of effective variational wave function ψ λ . We employ the Hubbard–Stratonovich method to decompose the interactions in terms of auxiliary fields and we use this in an expansion of the true ground-state wave function. The ground-state wave function is written as a linear combination of the basis states for which we diagonalize the Hamiltonian to obtain the lowest energy state.