AI 中文总结
研究均匀电子气静态交换基准，结合一阶局部场关系与精确静态交换极化率得出基准公式。通过对比发现不同方法精度差异，对QMC局部场因子分解表明两特征源于交换关联抵消，导出的交换核阈值能再现特定电荷阈值。
AI 中文摘要
均匀电子气的静态局部场因子可通过量子蒙特卡罗（QMC）计算精确得知，但其两个显著特征缺乏机制解释：G +在接近2kF之前几乎与q²成正比增长，费米面的剧烈2kF物理现象在其中仅留下微弱痕迹。结合教科书一阶局部场关系与精确静态交换极化率得到一个紧凑的精确基准：通用的仅交换局部场因子Gx(q,0) = -I(Q)Q²/L(Q)²，Q = q/2kF，在小q时精确值为(¼)(q/kF)²，在2kF时为π²/6，大q时为1/3，给出未极化气体的仅交换自旋平均接触值g(0) = 1/2。通过与该基准对比，发现1980年BDL表格在1.5kF以下精确到约百分之一，而2024年Nazarov和Silkin的McLachlan变分核在0.5kF以下仅精确到百分之二，在2kF时低1.74倍，其大q极限与接触约束不一致。对QMC局部场因子围绕精确基线进行自旋分辨分解表明，在基于QMC表示的分辨率和平滑度假设下，这两个特征都源于强烈的交换关联抵消。从封闭形式导出的静态交换核阈值在每个波矢处一致计算，再现了1980年数值获得并在2014年再次恢复的接近q = 1.94kF处的有限波矢电荷阈值rs≈10.6，误差为0.2%。
英文摘要
The exchange-only local field factor Gx(q,omega) of the uniform electron gas is exact and universal, a single curve at every density when q is measured in units of kF and omega in units of the Fermi energy. This paper assembles the known pieces of the static Gx(q,0) into one expression, evaluates it exactly at every wavevector, and releases it as a short Python module. It rises as (q/kF)^2/4, has a large peak of 1.99 just below 2kF, passes through the exact value pi^2/6 at 2kF, and tends to 1/3. Used alone in static linear response it predicts a spin density wave at rs = 4.96 and a charge density wave at rs = 10.62. Quantum Monte Carlo shows the gas has neither. Exchange enters the measured density and spin factors G+ and G- identically, so their difference, twice the antiparallel-spin factor, contains no exchange at all and is measured to be small and smooth through 2kF. Whatever removed the exchange peak is therefore in the parallel-spin channel, where everything beyond first-order exchange is large, negative, and mirrors the exchange peak. In the measured G+ the net removal is 40 to 48 percent of the peak at rs = 1 to 10. The stability of the metallic electron gas against exchange-driven density waves is a parallel-spin effect, and the decomposition shows where microscopic calculations of each channel should go.
Comments25 pages, 5 figures, 4 tables substantially revised; title changed from v1
