Title: A highly accurate procedure for computing globally optimal Wannier functions in one-dimensional crystalline insulators Show Chinese title

Title: 一种在二维晶体绝缘体中计算全局最优Wannier函数的高精度方法

Abstract: A standard task in solid state physics and quantum chemistry is the computation of localized molecular orbitals known as Wannier functions. In this manuscript, we propose a new procedure for computing Wannier functions in one-dimensional crystalline materials. Our approach proceeds by first performing parallel transport of the Bloch functions using numerical integration. Then a simple analytically computable correction is introduced to yield the optimally localized Wannier function. The resulting scheme is rapidly convergent and is proven to yield real-valued Wannier functions that achieve global optimality. The analysis in this manuscript can also be viewed as a proof of the existence of exponentially localized Wannier functions in one dimension. We illustrate the performance of the scheme by a number of numerical experiments. Show Chinese abstract

Abstract: 在固体物理和量子化学中，一个标准的任务是计算称为Wannier函数的局域分子轨道。 在本文中，我们提出了一种新的方法，用于计算一维晶体材料中的Wannier函数。 我们的方法首先通过数值积分对布洛赫函数进行并行传输。 然后引入一个简单且可解析计算的修正项，以得到最优局域化的Wannier函数。 该方法收敛迅速，并被证明能够产生实值的Wannier函数，并达到全局最优性。 本文中的分析也可以被视为一维情况下指数局域化Wannier函数存在性的证明。 我们通过一系列数值实验展示了该方法的性能。