Ferromagnetism in the Two Dimensionalt−t′Hubbard Model at the Van Hove Density

Using an improved version of the projection quantum Monte Carlo technique, we study the square-lattice Hubbard model with nearest-neighbor hopping $t$ and next-nearest-neighbor hopping $t^{\prime }$ by simulation of lattices with up to $20\times 20$ sites. For a given ${R=2t}^{\prime }/t$, we consider that filling which leads to a singular density of states of the noninteracting problem. For repulsive interactions, we find an itinerant ferromagnet (antiferromagnet) for $R=0.94\mathrm{}$ ( $R=0.2\mathrm{}$). This is consistent with the prediction of the $T$-matrix approximation, which sums the most singular set of diagrams.