CORRELATION HOLE OF THE SPIN-POLARIZED ELECTRON-GAS, WITH EXACT SMALL-WAVE-VECTOR AND HIGH-DENSITY SCALING
CORRELATION HOLE OF THE SPIN-POLARIZED ELECTRON-GAS, WITH EXACT SMALL-WAVE-VECTOR AND HIGH-DENSITY SCALING
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DOI：
10.1103/physrevb.44.13298
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发表时间：
1991-12-15
影响因子：
3.7
通讯作者：
PERDEW, JP
中科院分区：
文献类型：
--
作者：
WANG, Y;PERDEW, JP
对于密度n = nup + ndown = 3/4-pi-r（s）3 = pi-k（s）6/192，自旋极化率zeta =（nup-ndown）/n的均匀电子气，我们研究了关联空穴的傅里叶变换ρ（c）BAR（k，r（s），zeta），以及关联能ρ（c）（r（s），zeta）=整数0/无穷大dk ρ（c）BAR/pi. 在高密度（r（s）--> 0）极限下，我们发现一个简单的标度关系k（s）rho（c）BAR/pi-g2 --> f（z，zeta），其中z = k/gk（s），g = [（1 + zeta）2/3 +（1 - zeta）2/3]/2，f（z，1）= f（z，0）. 函数f（z，zeta）只有弱的zeta依赖性，它的小z展开式-3 z/pi（2）+ 4平方根3 z2/pi（2）+...也是任意r（s）或zeta的精确小波矢量（k -> 0）展开式。 出于这些考虑，并通过讨论的大波矢和低密度的限制，我们提出了两个Pade表示的rho（c）BAR在任何k，r（s），或zeta，一个内，一个超出随机相位近似（RPA）。 我们还证明了rho（c）RPABAR服从Misawa的自旋标度关系的推广，并且rho（c）RPA的低密度（r（s）->无穷大）极限约为r（s）-3/4.
For a uniform electron gas of density n = n up + n down = 3/4-pi-r(s)3 = pi-k(s)6/192 and spin polarization zeta = (n up - n down)/n, we study the Fourier transform rho(c)BAR(k,r(s),zeta) of the correlation hole, as well as the correlation energy epsilon(c)(r(s),zeta) = integral-0/infinity dk rho(c)BAR/pi. In the high-density (r(s) --> 0) limit, we find a simple scaling relation k(s)rho(c)BAR/pi-g2 --> f(z,zeta), where z = k/gk(s), g = [(1 + zeta)2/3 + (1 - zeta)2/3]/2, and f(z,1) = f(z,0). The function f(z,zeta) is only weakly zeta dependent, and its small-z expansion - 3z/pi(2) + 4 square-root 3z2/pi(2) + ... is also the exact small-wave-vector (k --> 0) expansion for any r(s) or zeta. Motivated by these considerations, and by a discussion of the large-wave-vector and low-density limits, we present two Pade representations for rho(c)BAR at any k, r(s), or zeta, one within and one beyond the random-phase approximation (RPA). We also show that rho(c)RPABAR obeys a generalization of Misawa's spin-scaling relation for epsilon(c)RPA, and that the low-density (r(s) --> infinity) limit of epsilon(c)RPA is approximately r(s)-3/4.