Variational Monte Carlo study of incommensurate antiferromagnetic phases in the two-dimensional Hubbard model

We use a variational Monte Carlo technique to study the ground state of the two-dimensional Hubbard model on a square lattice. We study the stability of the usual commensurate antiferromagnetic phase against the formation of domain walls for various system sizes, band filling, and Hubbard repulsion. An instability towards diagonal domain walls is found for the values of the Hubbard repulsion studied (U=4-10t). We compute the condensation energy of the holes in walls. Such an incommensurate antiferromagnetic phase is much stabler than any other solution. Whether paramagnetic or purely superconducting, but superconductivity is found still to coexist with incommensurate antiferromagnetism. We carefully compare our results with those of the Hartree-Fock model and shed some light on the limitations of the Hartree-Fock solutions.