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SCDM-k: localized orbitals for solids via selected columns of the density matrix. (English) Zbl 1375.81255
Summary: The recently developed selected columns of the density matrix (SCDM) method [A. Damle et al., “Compressed representation of Kohn-Sham orbitals via selected columns of the density matrix”, J. Chem. Theory Comput. 11, No. 4, 1463–1469 (2015; doi:10.1021/ct500985f)] is a simple, robust, efficient and highly parallelizable method for constructing localized orbitals from a set of delocalized Kohn-Sham orbitals for insulators and semiconductors with $$\Gamma$$ point sampling of the Brillouin zone. In this work, we generalize the SCDM method to Kohn-Sham density functional theory calculations with k-point sampling of the Brillouin zone, which is needed for more general electronic structure calculations for solids. We demonstrate that our new method, called SCDM-k, is by construction gauge independent and a natural way to describe localized orbitals. SCDM-k computes localized orbitals without the use of an optimization procedure, and thus, does not suffer from the possibility of being trapped in a local minimum. Furthermore, the computational complexity of using SCDM-k to construct orthogonal and localized orbitals scales as $$\mathcal{O}(N \log N)$$ where $$N$$ is the total number of k-points in the Brillouin zone. SCDM-k is therefore efficient even when a large number of k-points are used for Brillouin zone sampling. We demonstrate the numerical performance of SCDM-k using systems with model potentials in two and three dimensions.

##### MSC:
 81V70 Many-body theory; quantum Hall effect 82D37 Statistical mechanics of semiconductors
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