Finite-temperature evaluation of the Fermi density operator

A rational expansion of the Fermi density operator is proposed. This approach allows to calculate efficiently physical properties of fermionic systems at finite temperatures without solving an eigenvalue problem. Using N evaluations of the Green's function, the Fermi density operator can be approximated, subject to a given precision, in the energy interval from -A to infinity with A proportional to N. The presented method may become especially useful for electronic structure calculations involving the calculation of charge densities.