强定域量子晶体态的Jelvis模型
Strongly localized quantum crystalline states of the jellium model
摘要：
我们考虑一个由N个电子组成的系统与体积为V的立方体盒子内的中性正背景相互作用。在将盒子分成N（或N/2）个极化（非极化）立方体单元之后，我们用合适的权重函数对每个单元上的创建场算子进行平均，并且我们考虑通过让所有平均算子作用于真空态而获得的量子晶态。这些状态排除了在极化或非极化情况下每个电池可能暂时包含多于一个或两个电子的可能性。这类状态的哈密顿量的期望值在热力学极限中进行评估，并且以使期望值最小化的方式选择权函数。所涉及的数值分析是显式地进行与权重函数具有广义高斯形状取决于一个参数。结果表明，当rs>90和rs>28时，非极化和极化量子晶体态产生的每粒子能量分别小于均匀Hartree-Fock量子晶体态.此外，对于极化情况，在r_s=100处的每个粒子的能量为-0.01448ryd，接近于最佳量子蒙特卡罗值-0.0153530（8）ryd [Drummond等人，B { \bf 69}，085116，（2004）]，并且该差异测量了在我们的近似中忽略的相关贡献。
英文摘要：
We consider a system made up of N electrons interacting with a neutralizing positive background within a cubic box of volume V. After dividing the box into N (or N/2) cubic cells for the polarized (unpolarized) case, we average the creation field operator over each cell with a suitable weight function and we consider the quantum crystalline states obtained by letting all the average operators act on the vacuum state. These states exclude the possibility that each cell may momentarily contain more than one or two electrons in the polarized or unpolarized case. The expectation value of the Hamiltonian over this class of states is evaluated in the thermodynamic limit and the weight function is chosen in such a way to minimize the expectation value. The involved numerical analysis is explicitly performed with a weight function having a generalized Gaussian shape depending on a parameter. It turns out that the unpolarized and polarized quantum crystalline states yield an energy per particle smaller than the homogeneous Hartree-Fock ones for r_s>90 and r_s>28, respectively. Moreover, for the polarized case, the energy per particle at r_s=100 is -0.01448ryd close {to -0.0153530(8)ryd, the best quantum Monte Carlo value [Drummond et al., Phys. Rev.B {\bf 69}, 085116, (2004)] and this discrepancy measures the correlation contribution neglected in our approximation.
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