A high-order procedure for computing globally optimal Wannier functions in one-dimensional crystalline insulators

A standard task in solid state physics and quantum chemistry is the computation of localized molecular orbits 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, using novel analysis, we show that a simple correction can be analytically computed that yields the optimally localized Wannier function. The resulting scheme is robust and capable of achieving high-order accuracy. We illustrate this in a number of numerical experiments.