Graduate School of System Informatics, Kobe University, 1-1 Rokkodai, Nada, Kobe 657-8501, Japan.
J Chem Phys. 2016 Dec 7;145(21):214104. doi: 10.1063/1.4969071.
Correlational and thermodynamic properties of homogeneous electron liquids at finite temperatures are theoretically analyzed in terms of dielectric response formalism with the hypernetted-chain (HNC) approximation and its modified version. The static structure factor and the local-field correction to describe the strong Coulomb-coupling effects beyond the random-phase approximation are self-consistently calculated through solution to integral equations in the paramagnetic (spin unpolarized) and ferromagnetic (spin polarized) states. In the ground state with the normalized temperature θ=0, the present HNC scheme well reproduces the exchange-correlation energies obtained by quantum Monte Carlo (QMC) simulations over the whole fluid phase (the coupling constant r≤100), i.e., within 1% and 2% deviations from putative best QMC values in the paramagnetic and ferromagnetic states, respectively. As compared with earlier studies based on the Singwi-Tosi-Land-Sjölander and modified convolution approximations, some improvements on the correlation energies and the correlation functions including the compressibility sum rule are found in the intermediate to strong coupling regimes. When applied to the electron fluids at intermediate Fermi degeneracies (θ≈1), the static structure factors calculated in the HNC scheme show good agreements with the results obtained by the path integral Monte Carlo (PIMC) simulation, while a small negative region in the radial distribution function is observed near the origin, which may be associated with a slight overestimation for the exchange-correlation hole in the HNC approximation. The interaction energies are calculated for various combinations of density and temperature parameters ranging from strong to weak degeneracy and from weak to strong coupling, and the HNC values are then parametrized as functions of r and θ. The HNC exchange-correlation free energies obtained through the coupling-constant integration show reasonable agreements with earlier results including the PIMC-based fitting over the whole fluid region at finite degeneracies in the paramagnetic state. In contrast, a systematic difference between the HNC and PIMC results is observed in the ferromagnetic state, which suggests a necessity of further studies on the exchange-correlation free energies from both aspects of analytical theory and simulation.
在有限温度下，运用介电响应理论和超网链（HNC）近似及其修正形式，对均匀电子液体的相关和热力学性质进行了理论分析。通过求解顺磁（自旋非极化）和铁磁（自旋极化）状态下的积分方程，自洽地计算了静态结构因子和局部场修正，以描述超出随机相位近似的强库仑耦合效应。在归一化温度θ=0 的基态下，本 HNC 方案很好地再现了通过量子蒙特卡罗（QMC）模拟在整个流体相中获得的交换关联能（耦合常数 r≤100），即在顺磁和铁磁状态下，与假定的最佳 QMC 值分别相差 1%和 2%以内。与基于 Singwi-Tosi-Land-Sjölander 和修正卷积近似的早期研究相比，在中等到强耦合范围内，关联能和关联函数（包括压缩和求和规则）得到了一些改进。当应用于中等费米简并度（θ≈1）的电子液体时，HNC 方案计算的静态结构因子与路径积分蒙特卡罗（PIMC）模拟的结果吻合较好，而在原点附近观察到径向分布函数的一个小负区域，这可能与 HNC 近似中对交换关联空穴的略微高估有关。计算了各种密度和温度参数组合的相互作用能，范围从强简并到弱简并，从弱耦合到强耦合，并将 HNC 值参数化为 r 和θ 的函数。通过耦合常数积分得到的 HNC 交换关联自由能与早期结果，包括在顺磁状态下有限简并度的整个流体区域的 PIMC 拟合结果吻合较好。相比之下，在铁磁状态下观察到 HNC 和 PIMC 结果之间存在系统差异，这表明需要从分析理论和模拟两个方面进一步研究交换关联自由能。
