We have investigated the magnetism and pairing correlations of the triangular lattice based on the Hubbard model using the determinant quantum Monte Carlo method and the constrained path Monte Carlo. The results show that the presence of the next-nearest-neighbor hopping integral $t^{\prime }$ introduces an additional energy scale to the system, and through $t^{\prime }$, one can regulate the shape of the density of states and thus the position of the van Hove singularity point. Increasing inverse temperature $\beta$ and on-site interaction $U$ favor the formation of ferromagnetic correlation in a rather large filling region, and the calculations for different lattice sizes show that the range of the ferromagnetic correlations is smaller than the smallest lattice simulated at the investigated temperatures. We study the different pairing correlations of the triangular lattice near several typical fillings and show that the $f$-wave pairing dominates the system in the filling region near the van Hove singularity point with a high density of states, where the ferromagnetic correlation is also enhanced. When the filling is close to half-filling, the pairing susceptibility with $f$ wave is suppressed and the pairing susceptibility of $f_n$ wave is enhanced, however, both the effective pairing interaction with $f$ wave and $f_n$ wave are negative, which indicates that neither $f$-wave nor $f_n$-wave superconductivity may exist. Finally, we find that the pairing channel of different symmetry in the system maybe closely related to the magnetic properties. Ferromagnetic fluctuation favors the formation of $f$-wave pairing, while antiferromagnetic fluctuation tends to promote $f_n$-wave pairing.

中文翻译：

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可调谐范霍夫奇点附近的磁涨落和主导超导配对对称性

我们利用行列式量子蒙特卡罗方法和约束路径蒙特卡罗方法研究了基于哈伯德模型的三角晶格的磁性和配对相关性。结果表明，下一个最近邻跳跃积分的存在$t^{\prime }$向系统引入额外的能量尺度，并通过$t^{\prime }$，我们可以调节态密度的形状，从而调节范霍夫奇点的位置。增加逆温度$\beta$以及现场互动$U$有利于在相当大的填充区域中形成铁磁相关性，并且对不同晶格尺寸的计算表明，铁磁相关性的范围小于在研究温度下模拟的最小晶格。我们研究了几种典型填充物附近三角晶格的不同配对相关性，并表明$F$波对在范霍夫奇点附近的填充区域中占主导地位，具有高态密度，其中铁磁相关性也得到增强。当填充接近半填充时，配对磁化率$F$波被抑制，配对敏感性$F_n$波增强，然而，有效的配对相互作用$F$波和$F_n$波均为负值，这表明两者都没有$F$-波也不$F_n$波超导可能存在。最后，我们发现系统中不同对称性的配对通道可能与磁特性密切相关。铁磁波动有利于形成$F$-波配对，而反铁磁涨落往往会促进$F_n$-波配对。