Escobar Azor Miguel, Alves Estefania, Evangelisti Stefano, Berger J Arjan
Laboratoire de Chimie et Physique Quantiques, CNRS, Université Toulouse III (UPS), 118 Route de Narbonne, F-31062 Toulouse, France.
CEMES/CNRS, 29 Rue J. Marvig, 31055 Toulouse, France.
J Chem Phys. 2021 Sep 28;155(12):124114. doi: 10.1063/5.0063100.
In this work, we investigate the Wigner localization of two interacting electrons at very low density in two and three dimensions using the exact diagonalization of the many-body Hamiltonian. We use our recently developed method based on Clifford periodic boundary conditions with a renormalized distance in the Coulomb potential. To accurately represent the electronic wave function, we use a regular distribution in space of Gaussian-type orbitals and we take advantage of the translational symmetry of the system to efficiently calculate the electronic wave function. We are thus able to accurately describe the wave function up to very low density. We validate our approach by comparing our results to a semi-classical model that becomes exact in the low-density limit. With our approach, we are able to observe the Wigner localization without ambiguity.
在这项工作中，我们使用多体哈密顿量的精确对角化方法，研究了二维和三维中极低密度下两个相互作用电子的维格纳局域化。我们采用了最近开发的方法，该方法基于具有库仑势中重整化距离的克利福德周期性边界条件。为了精确表示电子波函数，我们在空间中使用高斯型轨道的规则分布，并利用系统的平移对称性来高效计算电子波函数。因此，我们能够精确描述直至极低密度的波函数。我们通过将结果与在低密度极限下变得精确的半经典模型进行比较来验证我们的方法。通过我们的方法，我们能够明确地观察到维格纳局域化。
