论文标题
Fermion晶格模型的功能重归其化组在三个维度上：在Cubic晶格上应用于Hubbard模型
Functional renormalization group for fermion lattice models in three dimensions: application to the Hubbard model on the cubic lattice
论文作者
论文摘要
迄今为止，迄今为止，通道定制的功能重新归一化组（FRG）方法最近已用于各种二维模型系统。然而，对于许多有趣的材料系统，第三个空间维度显然相关。因此，在三个空间维度（3D）中工作的FRG方案绝对是愿望清单。 Here we demonstrate that a 3D TUFRG scheme can be set up in straightforward extension of previous 2D codes and gives physically sensible results with affordable numerical effort, both regarding the qualitative as well as the quantitative description.三维Hubbard模型在半填充或完美嵌套时的计算相图显示，以\（（π，π，π）\）的相位过渡，有序的反铁磁基态在能量尺度上进行排斥性相互作用，可与文献中其他数值方法进行很好的比较。此外，该方法使我们能够检测一个\（d \） - 波配对和同意\（（（π，π，0）\）抗firomagnetic基态在孔掺杂的哈伯德模型中。
The channel-decomposed functional renormalization group (FRG) approach, most recently in the variant of truncated-unity-(TU-)FRG, has so far been used for various two-dimensional model systems. Yet, for many interesting material systems the third spatial dimension is of clear relevance. Therefore FRG schemes working in three spatial dimensions (3D) are definitely on the wishlist. Here we demonstrate that a 3D TUFRG scheme can be set up in straightforward extension of previous 2D codes and gives physically sensible results with affordable numerical effort, both regarding the qualitative as well as the quantitative description. The computed phase diagram of the three-dimensional Hubbard model at half filling or perfect nesting shows a phase transition to a \((π,π,π)\)-ordered antiferromagnetic ground state for repulsive interactions at an energy scale that compares well with other numerical approaches in the literature. Furthermore, the method allowed us to detect a \(d\)-wave pairing and a concurring \((π,π,0)\) antiferromagnetic ground state in the hole doped Hubbard model.
