论文标题
针对半填充的哈伯德模型具有非局部密度相互作用的量子量蒙特卡洛
Determinant quantum Monte Carlo for the half-filled Hubbard model with nonlocal density-density interactions
论文作者
论文摘要
我们设计了一种新型的形式主义，用于针对半填充的哈伯德模型的量子蒙特卡洛方法，其现场Hubbard相互作用$ U $和最接近的邻居密度相互作用$ V $在方形晶格上。形式主义对于$ | u | \ ge 4 | v | $没有符号问题，并且可以通过仅在最近的邻居债券上引入离散的辅助字段来实现。基于这种形式主义，我们使用投影仪算法系统地研究模型的基态相图。在符号问题中，免费参数空间$ | u | \ ge 4 | v | $，我们获得了$ u \ u \ ge 4 | v |> 0 $的抗fiferromagnetism，$ <-u <-4V $和$ v> 0 $的充电密度波和$ u <0 $和小型$ v $的$ u <0 $和$ u <0 $ u <0 $ u <0 $和一个较大的$ u <0 $ v $ v $ v $ v $ v $ v $ v $ v $ v $ v $ v $ v $ v $ v $ v $ v $ v $ v $ v $ v $ v $ v $ v $ v $ v $ v $ v $ v。我们还获得了单个粒子间隙和旋转激发光谱，并且与平均场结果以及可用文献相比，我们讨论了无标志 - 问题区域以外的可能的相边界。在未来的研究中，可以将公正的数值结果视为基准。最后，我们讨论了模型中长期相互作用的可能扩展。
We design a novel formalism of determinant quantum Monte Carlo method for the half-filled Hubbard model with on-site Hubbard interaction $U$ and nearest neighbor density-density interaction $V$ on the square lattice. The formalism is free of sign problem for $|U|\ge 4|V|$, and is achieved by introducing discrete auxiliary fields on the nearest-neighbor bonds alone. Based on this formalism, we study the ground state phase diagram of the model systematically using the projector algorithm. Within the sign-problem free parameter space $|U|\ge 4|V|$, we obtain antiferromagnetism for $U\ge 4|V|>0$, charge density wave for $U<-4V$ and $V>0$, s-wave superconductivity for $U<0$ and small negative $V$, and phase separation for $U<0$ and a larger negative $V$. We also obtain the single particle gap and spin excitation spectra, and by comparison to mean field results, as well as available literatures, we discuss the possible phase boundary beyond the sign-problem free region. The unbiased numerically exact results can be taken as benchmarks in future studies. Finally, we discuss possible extension for longer-range interactions in the model.
