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arXiv · 2409.04369

A highly accurate procedure for computing globally optimal Wannier functions in one-dimensional crystalline insulators

Abinand Gopal·Hanwen Zhang
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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.

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Abinand Gopal, Hanwen Zhang. 2024-09-06. A highly accurate procedure for computing globally optimal Wannier functions in one-dimensional crystalline insulators. https://arxiv.org/abs/2409.04369

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