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arXiv 0906.1344cond-mat.str-el
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具有纠缠能带结构的关联材料有效模型的从头算方法

Ab-initio procedure for effective models of correlated materials with entangled band structure

Takashi Miyake, Ferdi Aryasetiawan, Masatoshi Imada

摘要:

我们提出了一种第一性原理方法,用于推导具有纠缠能带结构的固体中电子的有效低能模型。该过程开始于将希尔伯特空间分成两个子空间,低能量部分("$d$空间")和空间的其余部分("$r$空间")。通过消除$r$空间的自由度,为$d$空间构造低能量模型。由此导出的模型包含由部分屏蔽的库仑相互作用表示的电子相关的强度,在约束随机相位近似(cRPA)中计算,其中减去$d$空间内的屏蔽通道,$P_d$。这种建立的下折方法的一个概念性问题是,对于纠缠带,不清楚如何切割出$d$空间以及如何从总偏振中区分$P_d$。在这里,我们提出了一个简单的程序来克服这个困难。在我们的方案中,$d$子空间是从Kohn Sham特征函数的Hilbert空间中切出的,并借助于一个构造局部Wannier基的过程。$r$子空间被构造为与$d$子空间正交的互补空间。在这种解纠缠之后,$P_d$变得明确。使用解纠缠带,在cRPA中唯一地确定有效参数。该方法成功地应用于3种$d$过渡金属的分析。

英文摘要:

We present a first-principles method for deriving effective low-energy models of electrons in solids having entangled band structure. The procedure starts with dividing the Hilbert space into two subspaces, the low-energy part ("$d$ space'') and the rest of the space ("$r$ space''). The low-energy model is constructed for the $d$ space by eliminating the degrees of freedom of the $r$ space. The thus derived model contains the strength of electron correlation expressed by a partially screened Coulomb interaction, calculated in the constrained random-phase-approximation (cRPA) where screening channels within the $d$ space, $P_d$, are subtracted. One conceptual problem of this established downfolding method is that for entangled bands it is not clear how to cut out the $d$ space and how to distinguish $P_d$ from the total polarization. Here, we propose a simple procedure to overcome this difficulty. In our scheme, the $d$ subspace is cut out from the Hilbert space of the Kohn Sham eigenfunctions with the help of a procedure to construct a localized Wannier basis. The $r$ subspace is constructed as the complementary space orthogonal to the $d$ subspace. After this disentanglement, $P_d$ becomes well defined. Using the disentangled bands, the effective parameters are uniquely determined in the cRPA. The method is successfully applied to 3$d$ transition metals.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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