2003/11/20 by Anders M. N. Niklasson · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Graph theory and applications #Matrix Theory and Algorithms #Theoretical and Computational Physics #cond-mat.mtrl-sci
paper · pdf · doi:10.1103/physrevb.68.233104
4 pages, 2 figures
arxiv created 2003/11/20 · openalex publication_date 2003/12/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An implicit purification scheme is proposed for calculation of the temperature-dependent, grand canonical single-particle density matrix, given as a Fermi-Dirac operator expansion in terms of the Hamiltonian. The computational complexity is shown to scale with the logarithm of the polynomial order of the expansion, or equivalently, with the logarithm of the inverse temperature. The system of linear equations that arise in each implicit purification iteration is solved efficiently by a conjugate gradient solver. The scheme is particularly useful in connection with linear scaling electronic structure theory based on sparse matrix algebra. The efficiency of the implicit temperature expansion technique is analyzed and compared to some explicit purification methods for the zero temperature density matrix.