论文标题
基于有效的作用形式主义的超流体系统密度功能理论的微观衍生
Microscopic derivation of density functional theory for superfluid systems based on effective action formalism
论文作者
论文摘要
超流体系统的密度功能理论是基于有效的动作形式主义的功能重归其化组的框架开发的。我们引入了针对粒子和非局部配对密度的有效作用，并证明了Hohenberg-kohn for Superfluid系统的定理是根据有效的作用而建立的。然后得出有效动作的流程方程，其中流参数从$ 0 $到$ 1 $，对应于非相互作用和交互系统。从平衡密度满足的流动方程和变异方程式中，我们获得了Kohn-Sham电位的确切表达，以概括为包括配对势。由此产生的Kohn-Sham电位具有不错的功能，可以单独表达外部，Hartree，配对和交换相关项的显微镜公式。结果表明，我们的Kohn-Sham电位通过忽略了相关性，从而赋予了Hartree-fock-Bogoliubov理论的基础能量。我们确切的形式主义的一个优点在于，它提供了系统地改善相关部分的方法。
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 nonlocal 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 from $0$ to $1$, 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 including the pairing potentials. The resultant Kohn-Sham potential has a nice feature 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 systematically improve the correlation part.
