论文标题
确切的绿色功能方法用于rkky互动
Exact Green's function approach to RKKY interactions
论文作者
论文摘要
精确地计算了嵌入在电子气体中的两个局部磁矩的绿色功能〜（GF）。电子在有效的质量近似中进行处理，并且磁矩与电子相互作用与电子相互作用耦合。由Slater-Koster和Ziman通过使用Woodbury身份的Slater-Koster和Ziman开发的方法，通过对Slater-Koster和Ziman开发的方法的概括来获得所得的GF。确切的GF至关重要地取决于原点上单电子GF的值，称为〜$ g_0 $。天生的系列只有在〜$ g_0 $是有限的情况下才会收敛，该$ g_0 $以〜$ 1D $的价格为抛物线能量带，但不得$ 2D $和〜$ 3D $。在一般情况下，确切的GF包括局部旋转操作员的非线性组合。给出了一种计算这些运算符的矩阵元素的方法。对于旋转〜$ s_a = s_b = 1/2 $，精确的GF表示为〜$ \ hs_a，\ hs_b $的组件的线性组合，而确切的范围函数〜$ {\ cal j}（r）$作为双重积分在分析表达上获得。对于电子能量〜$ e = 0 $和〜$ j g_0/2 = 2 $或〜$ j g_0/2 = -2/3 $范围函数和gf是单数的。 GF的电线发生在奇异点的效果中，并计算结合状态的产生能量。有三个政权〜$ j $。对于小$ j $，范围函数类似于rkky：它具有相同的时期〜$π/k_f $，相同的衰减字符和略有不同的幅度，通常在几个百分点之内。这种制度在本质上最常发生。对于〜$ | j | $可与〜$ | g_0 |^{ - 1} $相当，确切的范围函数与rkky One质量不同。对于大$ | J | $，确切的范围功能具有相同的时期和类似于功率的衰减的振荡，但随着增长〜$ | j | $的增长幅度衰减要低得多。
The Green's function~(GF) of two localized magnetic moments embedded in the electron gas is calculated exactly. The electrons are treated in the effective mass approximation and the magnetic moments are coupled with electrons by a delta-like~$s-d$ interaction. The resulting GF is obtained by the exact summation of the Born series using a generalization of the method developed by Slater-Koster and Ziman to non-commuting spin operators with the use of the Woodbury identities. The exact GF crucially depends on the value of the one-electron GF at the origin, denoted as~$g_0$. The Born series is convergent only if~$g_0$ is finite, which holds for electrons in parabolic energy bands in~$1D$, but not in~$2D$ and~$3D$. In the general case, the exact GF includes nonlinear combination of localized spins operators. A method of calculating matrix elements of these operators is given. For spins~$S_a=S_b = 1/2$ the exact GF is expressed as a linear combination of components of~$\hS_a, \hS_b$, and the exact range function~${\cal J}(r)$ is obtained as a double integral over analytical expression. For electron energy~$E=0$ and~$J g_0/2 = 2$ or~$J g_0/2=-2/3$ the range function and GF are singular. Poles of GF occur in the vicinities of singularity points and the resulting energies of bound states are calculated. There are three regimes of~$J$. For small $J$ the range function resembles RKKY one: it has the same period~$π/k_F$, the same decay character and a slightly different amplitude, usually within a few percent. This regime occurs for most frequently in the nature. For~$|J|$ comparable to~$|g_0|^{-1}$ the exact range function differs qualitatively from RKKY one,. For large $|J|$ the exact range function oscillates with the same period and power-like decay as the usual RKKY function but it has much lower amplitude decaying with growing~$|J|$.
