标题： 反称偶极幂的所需状态数仅随问题规模适度增加 显示英文标题

标题： Required number of states increases only moderately with the problem size for antisymmetrized geminal powers

摘要： 我们提出一种算法，使用反对称双电子幂的线性组合作为变分波函数，以获得多电子系统的基态能量。 我们优化了该算法，以获得多电子系统的能量和其他参数。 同时，我们明确了张量收缩中的总计算瓶颈，并成功减少了计算时间。 结果表明，我们可以使用扩展的双电子状态数量来获得水分子和 Hubbard 模型的基态。 使用 Dunning 双 zeta 基组的水分子的结果，其误差在精确对角化能量的毫哈特里以下。 此外，我们观察到具有 14 个格点的一维 Hubbard 模型的结果能够很好地捕捉正确的基态，而二维 Hubbard 模型的结果仍缺乏部分能量，这反映了希尔伯特空间的大小较大。 我们得出结论，为了获得足够准确的能量，双电子状态所需的项数仅适度受问题规模的影响。 我们进一步展示了在变分过程中双电子状态数值算法的其他技术细节。 预计随着使用更扩展的计算资源和更大的电子系统规模，我们的算法可以提供改进的结果。 显示英文摘要

摘要： We propose an algorithm to obtain the ground-state energy of a many-electron system using the variational wave function of a linear combination of antisymmetrized geminal powers. We optimized this algorithm to obtain the energy and the other parameters of a many-electron system. Also we clarified the bottleneck of the total calculation in the tensor contraction and successfully reduced the computational time. As a result, we can use an extended number of geminal states to obtain the ground state of the water molecule and Hubbard models. The result for the water molecule with the Dunning double-zeta basis is of the sub-milihartree order above the energy of exact diagonalization. Further, we observe that the result for the one-dimensional Hubbard model with 14 sites shows good tendency to capture the right ground state and that for the two-dimensional Hubbard model still lacks some part of the energy reflecting the large size of the Hilbert space. We conclude that the required number of terms for geminal states for sufficiently accurate energy is only moderately affected by the problem size. We further show other technical details for the numerical algorithms of geminal states in the variation process. It is expected that with the use of more extended computing resources and larger sizes of electronic systems, our algorithm can provide improved results.