Variational Monte Carlo Study of the Two-Dimensional Hubbard Model Using Slater-Jastrow Wave Functions

We present numerical results for the 2D Hubbard and Extended Hubbard models on a variety of lattices using Variational Monte Carlo with a generalized Slater-Jastrow ansatz. We employ stochastic optimization to determine the thousands of Jastrow parameters that parameterize the ground state. In order to fully characterize the ground state physics, we calculate correlation functions for larger lattice sizes than are tractable using projector QMC algorithms and use those results to perform finite-size scaling analyses. Our results support previous findings that the half-filled one-band Hubbard model undergoes a transition to an antiferromagnetic phase at an infinitesimally small value of the critical on-site repulsion. We also discuss the application of our method to ab initio Hamiltonians.