论文标题
任意维度的均质电子气
Homogeneous electron gas in arbitrary dimensions
论文作者
论文摘要
均质电子气体是凝结物理学中研究最多的模型系统之一。它也是密度功能理论功能的大部分近似值。因此，它的交换相关能量已经进行了广泛的研究，并且在1、2和3维的系统中众所周知。在这里，我们扩展了此模型并计算交换和相关能量，作为Wigner-Seitz Radius $ R_S $的函数，对于任意尺寸$ D $。我们发现缩小尺寸空间（$ d = 1 $和2），我们的三维空间以及更高维度的行为非常不同。实际上，对于$ d> 3 $，相关能量的主要术语并不取决于$ r_s $的对数（如$ d = 3 $），而是缩放多项式：$ -c_d /r_s^{γ_d} $，与指数$umγ_d=（d-3） /（d-3） /（d-3） /（d-d-1）$。在很大的$ d $限制中，发现$ c_d $的值与维度线性依赖。在此限制中，我们还发现交换和相关的概念合并，共享一个共同的$ 1/r_s $依赖性。
The homogeneous electron gas is one of the most studied model systems in condensed matter physics. It is also at the basis of the large majority of approximations to the functionals of density functional theory. As such, its exchange-correlation energy has been extensively studied, and is well-known for systems of 1, 2, and 3 dimensions. Here, we extend this model and compute the exchange and correlation energy, as a function of the Wigner-Seitz radius $r_s$, for arbitrary dimension $D$. We find a very different behavior for reduced dimensional spaces ($D=1$ and 2), our three dimensional space, and for higher dimensions. In fact, for $D > 3$, the leading term of the correlation energy does not depend on the logarithm of $r_s$ (as for $D=3$), but instead scales polynomialy: $ -c_D /r_s^{γ_D}$, with the exponent $γ_D=(D-3)/(D-1)$. In the large-$D$ limit, the value of $c_D$ is found to depend linearly with the dimension. In this limit, we also find that the concepts of exchange and correlation merge, sharing a common $1/r_s$ dependence.
