A method to calculate the one-body Green’s function for ground states of correlated electron materials is formulated by extending the variational Monte Carlo method. We benchmark against the exact diagonalization (ED) for the one- and two-dimensional Hubbard models of 16-site lattices, which proves high accuracy of the method. The application of the method to a larger-sized Hubbard model on the square lattice correctly reproduces the Mott insulating behavior at half-filling and gap structures of the $d$-wave superconducting state of the hole-doped Hubbard model in the ground state optimized by enforcing the charge uniformity, evidencing a wide applicability to strongly correlated electron systems. From the obtained $d$-wave superconducting gap of the charge-uniform state, we find that the gap amplitude at the antinodal point is several times larger than the experimental value when we employ a realistic parameter as a model of the cuprate superconductors. The effective attractive interaction of carriers in the $d$-wave superconducting state inferred for an optimized state of the Hubbard model is as large as the order of the nearest-neighbor transfer, which is far beyond the former expectation in the cuprates. We discuss the nature of the superconducting state of the Hubbard model in terms of the overestimate of the gap and the attractive interaction in comparison to the cuprates.

中文翻译：

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变分蒙特卡罗方法在单波谱函数中的应用

通过扩展变分蒙特卡罗方法，提出了一种计算相关电子材料基态单体格林函数的方法。我们针对16位格的一维和二维Hubbard模型的精确对角化（ED）进行了基准测试，证明了该方法的高精度。该方法在方格上的大型Hubbard模型中的应用正确地再现了半填充和间隙结构的Mott绝缘行为。$d$通过增强电荷均匀性，优化了基态中空穴掺杂的Hubbard模型的波超导状态，证明了其在强相关电子系统中的广泛适用性。从获得$d$在电荷均匀状态的超导波间隙中，我们发现当采用实际参数作为铜酸盐超导体模型时，反结点处的间隙幅度是实验值的几倍。载体中有效的吸引相互作用$d$为哈伯德模型的优化状态推断出的超导波状态与最近邻传递的阶数一样大，这远远超出了铜价的先前预期。我们根据间隙的高估和与铜酸盐相比吸引的相互作用来讨论哈伯德模型超导状态的性质。