Phase separation in the two-dimensional Hubbard model: A fixed-node quantum Monte Carlo study

Fixed-node Green’s-function Monte Carlo calculations have been performed for very large 16×16 two-dimensional Hubbard lattices, large interaction strengths U=10,20, and 40, and many (15∼20) densities between empty and half-filling. The nodes were fixed by a simple Slater-Gutzwiller trial wave function. For each value of U we obtained a sequence of ground-state energies which is consistent with the possibility of a phase separation close to half-filling, with a hole density in the hole-rich phase which is a decreasing function of U. The energies suffer, however, from a fixed-node bias: more accurate nodes are needed to confirm this picture. Our extensive numerical results and their test against size, shell, shape, and boundary-condition effects also suggest that phase separation is quite a delicate issue, on which simulations based on smaller lattices than considered here are unlikely to give reliable predictions.