Pole-Based Approximation of the Fermi-Dirac Function

Two approaches for the efficient rational approximation of the Fermi-Dirac function axe discussed: one uses the contour integral representation and conformal mapping, and the other is based on a version of the multipole representation of the Fermi-Dirac function that uses only simple poles. Both representations have logarithmic computational complexity. They are of great interest for electronic structure calculations.