AI 中文总结
该研究针对碳纳米管中少电子维格纳晶体的实验观测，采用从头算方法结合全组态相互作用，计算小型一维维格纳晶体的电子分布与交换耦合常数，结果与文献高度吻合。
AI 中文摘要
我们提出一种从头算（ab initio）方法，用于研究小型一维维格纳晶体的电子与磁学性质，尤其聚焦于电子电荷分布与交换耦合常数的计算。本研究的动机源于2019年《科学》（Science 364, 870）报道的碳纳米管中少电子维格纳晶体的实验观测结果。我们通过将电子限制在具有无限侧边势垒的一维势阱中，对实验装置进行建模；以斯莱特行列式（Slater determinants）为基组构建系统哈密顿量，并开展全组态相互作用计算，以确保在给定基组下捕获所有电子关联效应。作为单粒子基组，我们采用粒子在盒子中的波函数，其天然满足边界条件。利用该方法，我们获得了小型一维维格纳晶体的精确电子密度分布，这些分布清晰显示出电子的局域化特征。最后，我们提出一种将从头算方法映射到海森堡（Heisenberg）哈密顿量上的简单方法，以获取交换耦合常数；我们以维格纳二聚体为例对该方法进行验证，所得结果与文献中的结果吻合度极高。
英文摘要
We present an \emph{ab initio} method to study the electronic and magnetic properties of small one-dimensional Wigner crystals. In particular, we focus on the calculation of the electronic charge distribution and the exchange coupling constant. Our theoretical studies are motivated by the experimental observation of few-electron Wigner crystals in a carbon nanotube [Science 364, 870 (2019)]. We model the experimental setup by confining electrons in a one-dimensional potential well with infinite side barriers. We represent the Hamiltonian of the system in a basis of Slater determinants and perform full configuration interaction to ensure we capture all the electron correlation for a given basis set. As the one-particle basis set we use particle-in-a-box wave functions which by construction satisfy the boundary conditions. With our approach, we obtain accurate electronic density profiles of small one-dimensional Wigner crystals. These profiles clearly show the localisation of the electrons. Finally, we present a simple approach to obtain the exchange coupling constant by mapping our \textit{ab initio} method on a Heisenberg Hamiltonian. We illustrate our approach on a Wigner dimer. We obtain excellent agreement with a result in the literature.
Comments10 pages, 5 figures
