Low-energy effective interactions beyond cRPA by the functional renormalization group
Low-energy effective interactions beyond cRPA by the functional renormalization group
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DOI：
10.1103/physrevb.92.045113
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发表时间：
2015-03
期刊：
影响因子：
--
通讯作者：
M. Kinza;C. Honerkamp
中科院分区：
文献类型：
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作者：
M. Kinza;C. Honerkamp
在推导以费米能级附近能带为目标的固体低能有效模型时，约束随机相位近似（constrained random phase approximation，cRPA）已成为计算有效相互作用的有效工具。Wick有序约束泛函重整化群（cfRG）通过以无偏的方式包括所有相互作用通道来推广cRPA方法。在这里，我们提出了应用程序的cfRG两个简单的多频带系统，并比较所产生的有效的相互作用的cRPA。首先，我们考虑单层石墨烯的多带模型，其中我们整合出$\ensuremath{\sigma}$带，以获得$\ensuremath{\pi}$带的有效理论。事实证明，超出cRPA的项被带的不同的$xy$-平面反射对称性强烈抑制。在我们的模型中，当稍微干扰这种对称性差异时，cfRG对cRPA的修正变得可见，但是没有质的变化。这项研究表明，嵌入或分层的二维电子系统可以改变有效的相互作用参数超出预期的筛选考虑。第二个例子是一个一维模型的双原子系统让人想起一个CuO链，在那里我们考虑一个有效的理论Cu $3d$-类轨道。在此，fRG数据显示了与cRPA结果相比的相关和定性校正。我们认为，新的相互作用项影响的低能量模型的磁性。
In the derivation of low-energy effective models for solids targeting the bands near the Fermi level, the constrained random-phase approximation (cRPA) has become an appreciated tool to compute the effective interactions. The Wick-ordered constrained functional renormalization group (cfRG) generalizes the cRPA approach by including all interaction channels in an unbiased way. Here we present applications of the cfRG to two simple multiband systems and compare the resulting effective interactions to the cRPA. First, we consider a multiband model for monolayer graphene, where we integrate out the $\ensuremath{\sigma}$ bands to get an effective theory for $\ensuremath{\pi}$ bands. It turns out that terms beyond cRPA are strongly suppressed by the different $xy$-plane reflection symmetry of the bands. In our model the cfRG corrections to cRPA become visible when one disturbs this symmetry difference slightly, however, without qualitative changes. This study shows that the embedding or layering of two-dimensional electronic systems can alter the effective interaction parameters beyond what is expected from screening considerations. The second example is a one-dimensional model for a diatomic system reminiscent of a CuO chain, where we consider an effective theory for Cu $3d$-like orbitals. Here the fRG data shows relevant and qualitative corrections compared to the cRPA results. We argue that the new interaction terms affect the magnetic properties of the low-energy model.