Numerical construction of Wannier functions through homotopy

Abstract

We provide a mathematically proven, simple and efficient algorithm to build localised Wannier functions, with the only requirement that the system has vanishing Chern numbers. Our algorithm is able to build localised Wannier for topological insulators such as the Kane-Mele model. It is based on an explicit and constructive proof of homotopies for the unitary group. We provide numerical tests validating the methods for several systems, including the Kane-Mele model.

References in corpus (5)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Wannier representation of Z_2 topological insulators
• Exponential localization of Wannier functions in insulators
• Order-N implementation of exact exchange in extended systems
• Automated construction of maximally localized Wannier functions for bands with nontrivial topology

Cited by in corpus (5)

• The Wannier Function Software Ecosystem for Materials Simulations
• Projectability disentanglement for accurate and automated electronic-structure Hamiltonians
• Automated mixing of maximally localized Wannier functions into target manifolds
• Symmetric Fermi projections and Kitaev's table: topological phases of matter in low dimensions
• Topology vs localization in synthetic dimensions