Compressed Wannier modes found from an L₁ regularized energy functional

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We propose a method for calculating Wannier functions of periodic solids directly from a modified variational principle for the energy, subject to the requirement that the Wannier functions are orthogonal to all their translations ("shift-orthogonality"). Localization is achieved by adding an L₁ regularization term to the energy functional. This approach results in "compressed" Wannier modes with compact support, where one parameter μ controls the trade-off between the accuracy of the total energy and the size of the support of the Wannier modes. Efficient algorithms for shift-orthogonalization and solution of the variational minimization problem are demonstrated.