Implicit Purification for Temperature-Dependent Density Matrices

Details Implicit Purification for Temperature-Dependent Density Matrices Implicit Purification for Temperature-Dependent Density Matrices

2003-11-20

arxiv.org/abs/cond-mat/0311469v1

Physics

Condensed Matter

Materials Science

4 pages, 2 figures

Scientific paper

10.1103/PhysRevB.68.233104

An implicit purification scheme is proposed for calculation of the temperature-dependent, grand canonical single-particle density matrix, given as a Fermi 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.

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