一维哈伯德模型格林函数理论中的Löwdin对称性困境
Löwdin's symmetry dilemma within Green functions theory for the one-dimensional Hubbard model
摘要：
用解析方法和密度矩阵重整化群（DMRG）方法研究了一维关联Hubbard团簇的能隙.然而，在一维以上，量子蒙特卡罗方法只能对小系统得到精确的结果。由于这个原因，由于DMRG在模拟2D和3D系统时的问题，替代方法，如格林函数结合多体近似（GFMBA），没有这种限制，是非常重要的。然而，GFMBA模拟的近似特征是否阻止了哈伯德间隙的计算仍然是开放的。在这里，我们提出了新的GFMBA结果表明，GFMBA模拟能够产生可靠的数据的差距，以及同意与DMRG基准在1D。一个有趣的观察是，当模拟放弃精确系统的某些对称性限制时，如自旋对称性和空间均匀性，可以显着提高间隙的精度。这被看作是表现和推广的“对称性困境”介绍了Löwdin的哈特里-福克波函数计算。
英文摘要：
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.
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