Functional renormalization group for fermion lattice models in three dimensions: Application to the Hubbard model on the cubic lattice
Functional renormalization group for fermion lattice models in three dimensions: Application to the Hubbard model on the cubic lattice
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DOI：
10.1103/physrevb.102.195108
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发表时间：
2020-04
影响因子：
3.7
通讯作者：
J. Ehrlich;C. Honerkamp
中科院分区：
文献类型：
--
作者：
J. Ehrlich;C. Honerkamp
通道分解的功能重整化群（FRG）的方法，最近提出的截断单位FRG（TUFRG）的变体，迄今已被用于各种二维模型系统。然而，对于许多有趣的物质系统来说，第三个空间维度显然是相关的。因此，在三维空间（3D）中工作的FRG方案肯定在愿望清单上。在这里，我们证明了一个3D TUFRG计划可以建立在一个简单的扩展以前的二维码，并给出物理上合理的结果与负担得起的数值努力，关于定性和定量的描述。计算的三维哈伯德模型在半填充或完美嵌套的相图显示了一个相变到$（\ensuremath{\pi}，\ensuremath{\pi}，\ensuremath{\pi}）$-有序反铁磁基态的排斥相互作用的能量尺度，以及在文献中的其他数值方法比较。此外，该方法使我们能够检测到$d$波配对和并发$（\ensuremath{\pi}，\ensuremath{\pi}，0）$反铁磁基态的空穴掺杂的Hubbard模型。
The channel-decomposed functional renormalization group (FRG) approach, most recently presented in the variant of truncated-unity FRG (TUFRG), 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 wish list. Here we demonstrate that a 3D TUFRG scheme can be set up in a straightforward extension of previous two-dimensional codes and gives physically sensible results with affordable numerical effort, regarding both the qualitative and quantitative descriptions. The computed phase diagram of the three-dimensional Hubbard model at half filling or perfect nesting shows a phase transition to a $(\ensuremath{\pi},\ensuremath{\pi},\ensuremath{\pi})$-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 $(\ensuremath{\pi},\ensuremath{\pi},0)$ antiferromagnetic ground state in the hole-doped Hubbard model.