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

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 proven to produce globally optimal Wannier functions. 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.