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Numerical construction of Wannier functions through homotopy. (English) Zbl 1417.82030

Summary: 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 to validate the methods for several systems, including the Kane-Mele model.{
©2019 American Institute of Physics}

MSC:

82D20 Statistical mechanics of solids
82D25 Statistical mechanics of crystals
82B80 Numerical methods in equilibrium statistical mechanics (MSC2010)
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
81V70 Many-body theory; quantum Hall effect

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