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.

翻译：固体物理学和量子化学中的一个标准任务是计算被称为Wannier函数的局域化分子轨道。本文提出了一种计算一维晶体材料中Wannier函数的新方案。我们的方法首先通过数值积分对布洛赫函数进行平行移动，随后引入一个可解析计算的简单修正项，从而得到最优局域化的Wannier函数。该方案具有快速收敛性，并被证明能产生实现全局最优性的实值Wannier函数。本文的分析亦可视为对一维指数局域化Wannier函数存在性的证明。我们通过若干数值实验展示了该方案的性能。