The energy gap of correlated Hubbard clusters is well studied for one-dimensional systems using analytical methods and density-matrix-renormalization-group (DMRG) simulations. Beyond 1D, however, exact results are available only for small systems by quantum Monte Carlo. For this reason and, due to the problems of DMRG in simulating 2D and 3D systems, alternative methods such as Green functions combined with many-body approximations (GFMBA), that do not have this restriction, are highly important. However, it has remained open whether the approximate character of GFMBA simulations prevents the computation of the Hubbard gap. Here we present new GFMBA results that demonstrate that GFMBA simulations are capable of producing reliable data for the gap which agrees well with the DMRG benchmarks in 1D. An interesting observation is that the accuracy of the gap can be significantly increased when the simulations give up certain symmetry restriction of the exact system, such as spin symmetry and spatial homogeneity. This is seen as manifestation and generalization of the “symmetry dilemma” introduced by Löwdin for Hartree–Fock wave function calculations.

中文翻译：

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一维哈伯德模型的格林函数理论中的洛丁对称困境

使用分析方法和密度矩阵重整化群 (DMRG) 模拟对一维系统的相关哈伯德星团的能隙进行了很好的研究。然而，在 1D 之外，精确的结果仅适用于量子蒙特卡罗的小型系统。出于这个原因，并且由于 DMRG 在模拟 2D 和 3D 系统中的问题，没有此限制的替代方法（如格林函数与多体近似（GFMBA）相结合）非常重要。然而，GFMBA 模拟的近似特征是否会阻止哈伯德间隙的计算仍然是开放的。在这里，我们展示了新的 GFMBA 结果，证明 GFMBA 模拟能够为差距产生可靠的数据，这与一维 DMRG 基准非常吻合。一个有趣的观察结果是，当模拟放弃精确系统的某些对称性限制（例如自旋对称性和空间均匀性）时，间隙的精度可以显着提高。这被视为 Löwdin 为 Hartree-Fock 波函数计算引入的“对称困境”的表现和概括。