Expansion algorithm for the density matrix

Details Expansion algorithm for the density matrix Expansion algorithm for the density matrix

2002-09-20

arxiv.org/abs/cond-mat/0209502v1

Physics

Condensed Matter

Materials Science

5 pages, 4 figures, to appear in Phys. Rev. B

Scientific paper

10.1103/PhysRevB.66.155115

A purification algorithm for expanding the single-particle density matrix in terms of the Hamiltonian operator is proposed. The scheme works with a predefined occupation and requires less than half the number of matrix-matrix multiplications compared to existing methods at low (<10%) and high (>90%) occupancy. The expansion can be used with a fixed chemical potential in which case it is an asymmetric generalization of and a substantial improvement over grand canonical McWeeny purification. It is shown that the computational complexity, measured as number of matrix multiplications, essentially is independent of system size even for metallic materials with a vanishing band gap.

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