Compressed Wannier modes found from an $L_1$ regularized energy   functional
  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 $L_1$ regularization term to the energy functional. This approach results in "compressed" Wannier modes with compact support, where one parameter $\mu$ 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. 
Farzin Barekat, Ke Yin, Russel E. Caflisch, Stanley J. Osher, Rongjie   Lai and Vidvuds Ozolins
cond-mat.mtrl-sci math-ph math.MP quant-ph