Microscopic derivation of density functional theory for superfluid systems based on effective action formalism
Microscopic derivation of density functional theory for superfluid systems based on effective action formalism
复制标题
基于有效作用形式主义的超流系统密度泛函理论微观推导
DOI：
10.1093/ptep/ptaa173
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发表时间：
2021
影响因子：
3.5
通讯作者：
Kunihiro Teiji
中科院分区：
文献类型：
--
作者：
Yokota Takeru;Kasuya Haruki;Yoshida Kenichi;Kunihiro Teiji
在基于有效作用量理论的泛函重整化群框架下，发展了超流系统的密度泛函理论。我们引入了粒子数和非定域配对密度的有效作用量，并证明了超流系统的Hohenberg-Kohn定理是在有效作用量下成立的.然后推导出有效作用的流动方程，其中流动参数从到，对应于非相互作用和相互作用系统。从平衡密度所满足的流动方程和变分方程出发，得到了推广到包含对势的Kohn-Sham势的精确表达式。所得到的Kohn-Sham势具有一个很好的特点，即它分别表示了外部项、Hartree项、配对项和交换关联项的微观公式。结果表明，我们的Kohn-Sham势在忽略相关性的情况下给出了Hartree-Fock-Bogoliubov理论的基态能量。我们的精确形式主义的一个优点在于，它提供了系统地改进相关部分的方法。
A density-functional theory for superfluid systems is developed in the framework of the functional renormalization group based on the effective action formalism. We introduce the effective action for the particle-number and non-local pairing densities and demonstrate that the Hohenberg–Kohn theorem for superfluid systems is established in terms of the effective action. The flow equation for the effective action is then derived, where the flow parameter runs fromto, corresponding to the non-interacting and interacting systems. From the flow equation and the variational equation that the equilibrium density satisfies, we obtain the exact expression for the Kohn–Sham potential generalized to include the pairing potentials. The resultant Kohn–Sham potential has a nice feature in that it expresses the microscopic formulae of the external, Hartree, pairing and exchange–correlation terms separately. It is shown that our Kohn–Sham potential gives the ground-state energy of the Hartree–Fock–Bogoliubov theory by neglecting the correlations. An advantage of our exact formalism lies in the fact that it provides ways to improve the correlation part systematically.