Robust determination of maximally localized Wannier functions

We propose an algorithm to determine maximally localized Wannier functions (MLWFs). This algorithm, based on recent theoretical developments, does not require any physical input such as initial guesses for the Wannier functions, unlike popular schemes based on the projection method. We discuss how the projection method can fail on fine grids when the initial guesses are too far from MLWFs. We demonstrate that our algorithm is able to find localized Wannier functions through tests on two-dimensional systems, simplified models of semiconductors, and realistic DFT systems by interfacing with the wannier90 code. We also test our algorithm on the Haldane and Kane-Mele models to examine how it fails in the presence of topological obstructions