Abstract: The so-called Wannier localization problem in quantum physics is analogous to finding a localized representation of a subspace associated with a nonlinear eigenvalue problem and plays an important role in Hartree-Fock and Kohn-Sham density functional theory calculations. While this problem is well studied for insulating systems and good algorithms exist, considerably less is known for metallic systems with entangled eigenvalues. We propose a new, unified method to solve the Wannier localization problem that works in both the isolated and entangled setting. Our method is robust, direct, efficient, and does not require an initial guess. We will demonstrate the effectiveness of our methodology at constructing localized basis functions that may subsequently be used for Wannier interpolation of band structure.

Bio: Anil Damle is an assistant professor of Computer Science at Cornell University where he works at the intersection of numerical linear algebra and a broad range of application areas. His work includes the development of efficient and robust algorithms that leverage the underlying physical and/or statistical structure of problems. Anil received his BS and MS from the University of Colorado, Boulder in 2011 and his Ph.D. from Stanford University in 2016.