Grossi Juri, Musslimani Ziad H, Seidl Michael, Gori-Giorgi Paola
Department of Chemistry & Pharmaceutical Sciences and Amsterdam Institute of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands.
Department of Mathematics, Florida State University, Tallahassee, FL 32306-4510, United States of America.
J Phys Condens Matter. 2020 Aug 27;32(47). doi: 10.1088/1361-648X/abace2.
We re-adapt a spectral renormalization method, introduced in nonlinear optics, to solve the Kohn-Sham (KS) equations of density functional theory, with a focus on functionals based on the strictly-correlated electrons (SCE) regime, which are particularly challenging to converge. Important aspects of the method are: (i) the eigenvalues and the density are computed simultaneously; (ii) it converges using randomized initial guesses; (iii) easy to implement. Using this method we could converge for the first time the Kohn-Sham equations with functionals that include the next leading term in the strong-interaction limit of density functional theory, the so called zero-point energy (ZPE) functional as well as with an interaction-strength-interpolation functional that includes both the exact SCE and ZPE terms. This work is the first building block for future studies on quantum systems confined in low dimensions with different statistics and long-range repulsions, such as localization properties of fermions and bosons with strong long-range repulsive interactions in the presence of a random external potential.
我们重新采用了一种在非线性光学中引入的谱重整化方法，来求解密度泛函理论的科恩 - 沙姆（KS）方程，重点关注基于严格关联电子（SCE） regime的泛函，这类泛函在收敛方面极具挑战性。该方法的重要方面包括：（i）同时计算本征值和密度；（ii）使用随机初始猜测值收敛；（iii）易于实现。使用此方法，我们首次能够收敛包含密度泛函理论强相互作用极限中的次主导项（即所谓的零点能量（ZPE）泛函）以及包含精确SCE和ZPE项的相互作用强度插值泛函的科恩 - 沙姆方程。这项工作是未来关于具有不同统计特性和长程排斥作用的低维量子系统研究的首个基石，例如在随机外部势存在的情况下，具有强长程排斥相互作用的费米子和玻色子的局域化性质。
