Projector quantum Monte Carlo calculations are used to examine superconducting correlations in the two-dimensional Hubbard model with exponentially decaying electron hopping amplitudes $t_{ij}\left(q\right)\sim -q^{|{\mathbf{R}}_{\mathbf{i}}-{\mathbf{R}}_{\mathbf{j}}|}$. It is shown that this type of hopping, which models more realistically (in comparison to the nearest-neighbor hopping) the situation in real transition-metal materials, stabilizes significantly the superconducting correlations in the $d$-wave channel for electron concentrations $n$ above the quarter band filling, especially for $q\sim 0.35$. In this region the enhancement of the superconducting correlations at non-zero $q$, against the classical Hubbard limit ($q=0$), changes (depending on the electron concentration) from 2 in the worse case to 5 in the best case. Moreover, we have studied also the influence of the Coulomb interaction $U$ and a disorder on superconducting correlations. We have found that the Coulomb interaction enhances significantly superconducting correlations in the $d$-wave channel, while a disorder suppresses them gradually, but they surprisingly persist up to the disorder strength comparable to the Coulomb interaction.

投影量子蒙特卡罗计算用于检查二维哈伯德模型中的超导相关性，电子跳跃幅度呈指数衰减${吨}_{\mathrm{一世}j}\left(q\right)～-q^{|{\mathbf{R}}_{\mathbf{一世}}-{\mathbf{R}}_{\mathbf{j}}|}$. 结果表明，这种类型的跳跃更真实地模拟了真实过渡金属材料中的情况（与最近邻跳跃相比），显着稳定了超导相关性$d$电子浓度的波通道$n$以上四分之一带填充，特别是对于$q～0.35$. 在该区域中，非零超导相关性的增强$q$, 反对经典的哈伯德极限 ($q=0$)，变化（取决于电子浓度）从最坏情况下的 2 到最好情况下的 5。此外，我们还研究了库仑相互作用的影响$ü$和超导相关性的紊乱。我们发现库仑相互作用显着增强了超导相关性$d$波通道，虽然无序会逐渐抑制它们，但它们令人惊讶地持续到与库仑相互作用相当的无序强度。