二维和三维Wigner定域：\emph{ab initio}方法
Wigner localization in two and three dimensions: an \emph{ab initio} approach
摘要：
在这项工作中，我们研究了两个相互作用的电子在非常低的密度在二维和三维的维格纳局域化使用的多体哈密顿量的精确对角化。我们使用我们最近开发的方法的基础上Clifford周期性边界条件与库仑势的重整化距离。为了精确地表示电子波函数，我们使用高斯型轨道在空间中的规则分布，并且我们利用系统的平移对称性来有效地计算电子波函数。因此，我们能够精确地描述波函数，直到非常低的密度。我们通过将我们的结果与在低密度极限中变得精确的半经典模型进行比较来验证我们的方法。我们的方法，我们能够观察到的维格纳本地化没有歧义。
英文摘要：
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.
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