Two-dimensional Hubbard model with nearest- and next-nearest-neighbor hopping

作者：H. Q. Lin, J. E. Hirsch · 发表于：Physical review. B, Condensed matter · 年份：1987 · DOI：10.1103/physrevb.35.3359 · 被引用次数：184 · 研究领域：Physics of Superconductivity and Magnetism、Quantum and electron transport phenomena、Iron-based superconductors research

We study the magnetic properties of the two-dimensional Hubbard model with nearest-neighbor (t) and next-nearest-neighbor (${t}_{2}$) hopping and on-site repulsion U. We first calculate the mean-field phase diagram as a function of band filling and U. Because of the Van Hove singularity in the density of states, we find a ferromagnetic phase extending to zero U for certain band filling. For the half-filled band case, antiferromagnetism sets in at a finite value of U if ${t}_{2}$\ensuremath{\ne}0. We study the behavior of spin-spin correlation functions for small lattices of up to N=64 atoms using Monte Carlo simulations, as well as exact diagonalization for N=4. Our results show enhanced ferromagnetic correlations in some regions, but apparently no ferromagnetic long-range order. In the half-filled case, our numerical results are consistent with a nonzero critical U. For a non-half-filled band our results suggest that there is no long-range order.