Institute for Theoretical and Applied Electrodynamics, Russian Academy of Sciences, Izhorskaya 13, 125412 Moscow, Russia.
J Phys Condens Matter. 2011 Feb 16;23(6):065601. doi: 10.1088/0953-8984/23/6/065601. Epub 2011 Jan 20.
The Hubbard-I approximation is generalized to allow for direct evaluation of the equal-time anomalous two-electron propagator for the Hubbard model on a two-dimensional square lattice. This propagator is compared against the quantum Monte Carlo data obtained by Aimi and Imada (2007 J. Phys. Soc. Japan 76 113708) in the limit of strong electron-electron interaction. The Hubbard-I predictions are in good qualitative agreement with the Monte Carlo results. In particular, d-wave correlations decay as cr( - 3) ('free-electron' behaviour) if the separation r exceeds 2-3 lattice constants. However, the Hubbard-I approximation underestimates the coefficient c by a factor of about 3. We conclude that the Hubbard-I approximation, despite its simplicity and artefacts, captures the qualitative behaviour of the two-particle propagator for the Hubbard model, at least for moderate values of r.
哈伯德-I 近似被推广到可以直接评估 Hubbard 模型在二维正方形晶格上的等时反常双电子传播子。将这个传播子与 Aimi 和 Imada（2007 J. Phys. Soc. Japan 76 113708）在强电子-电子相互作用极限下通过量子蒙特卡罗方法得到的数据进行比较。哈伯德-I 预测与蒙特卡罗结果具有良好的定性一致性。特别是，如果分离 r 超过 2-3 个晶格常数，d 波相关性就会像 cr( - 3)（“自由电子”行为）一样衰减。然而，哈伯德-I 近似低估了系数 c 约 3 倍。我们得出结论，尽管哈伯德-I 近似存在简单性和人为因素，但它至少在 r 的中等值范围内捕捉到了 Hubbard 模型的双粒子传播子的定性行为。
