Finite-Temperature Evaluation of the Fermi Density Operator

A rational expansion of the Fermi density operator is proposed. This approach allows us to calculate efficiently the physical properties of fermionic systems at finite temperatures without solving an eigenvalue problem. UsingNevaluations of the Green's function, the Fermi density operator can be approximated, subject to a given precision, in the energy interval [β, ∞] with β ∝ N. The presented method may become especially useful for electronic structure calculations involving the calculation of charge densities, but it may also find other applications in, e.g., signal processing and numerical linear algebra.