Communication: Padé spectrum decomposition of Fermi function and Bose function

Abstract

Padé approximant is exploited for an efficient sum-over-poles decomposition of Fermi and Bose functions. The resulting poles are all pure imaginary and can therefore be used to define Padé frequencies, in analogy with the celebrated Matsubara frequencies. The proposed Padé spectrum decomposition is shown to be equivalent to a truncated continued fraction. It converges significantly faster than other schemes such as the Matsubara expansion at all temperatures. By introducing the characteristic validity length as the measure of approximant, we analyze the convergence properties of different schemes thoroughly. Our results qualify the present scheme the best among all sum-over-poles approaches. Thus, it is of great value in efficient numerical evaluations of integrals involving Fermi/Bose function in various condensed-phase matter problems.