任意维度下的均匀电子液：采用Singwi-Tosi-Land-Sjölander方法的交换与关联作用
Homogeneous Electron Liquid in Arbitrary Dimensions: Exchange and Correlation Using the Singwi-Tosi-Land-Sjölander Approach
AI总结：
本研究将均匀电子液模型推广至任意整数维度，采用STLS方法计算RPA之外的关联能，发现高维下STLS比RPA更符合求和规则，还明确了等离激元对该理论的重要作用。
摘要：
均匀电子气与均匀电子液的基态是量子物理与量子化学领域的核心基础模型，属于密度缓变区间的典型体系，该区间内的交换关联能可通过多种方法估算。在高密度条件下，一维、二维、三维体系的能量行为已被充分探明。本研究将该模型推广至任意整数维度，采用Singwi、Tosi、Land与Sjölander提出的经典STLS方法，计算了随机相位近似（RPA）之外的关联能；已知STLS方法在描述二维（2D）和三维（3D）体系顺磁与铁磁基态的全电子密度响应方面精度优异。针对更高维度，我们将STLS方法得到的关联能结果与此前RPA方法的计算值进行了对比，发现高维度下STLS方法的物理合理性更强，表现为该理论能更好地满足知名的求和规则。此外，我们还阐明了等离激元贡献对STLS理论的重要性。
英文摘要：
The ground states of the homogeneous electron gas and the homogeneous electron liquid are cornerstones in quantum physics and chemistry. They are archetypal systems in the regime of slowly varying densities in which the exchange-correlation energy can be estimated with a myriad of methods. For high densities, the behavior of the energy is well-known for 1, 2, and 3 dimensions. Here, we extend this model to arbitrary integer dimensions, and compute its correlation energy beyond the random phase approximation (RPA), using the celebrated approach developed by Singwi, Tosi, Land, and Sjölander (STLS), which is known to be remarkably accurate in the description of the full electronic density response for $2D$ and $3D$, both in the paramagnetic and ferromagnetic ground states. For higher dimensions, we compare the results obtained for the correlation energy using the STLS method with the values previously obtained using RPA. We found that at high dimensions STLS tends to be more physical in the sense that the infamous sum rules are better satisfied by the theory. We furthermore illustrate the importance of the plasmon contribution to STLS theory.
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