Multipole representation of the Fermi operator with application to the electronic structure analysis of metallic systems

We propose a multipole representation of the Fermi-Dirac function and the Fermi operator and use this representation to develop algorithms for electronic structure analysis of metallic systems. The algorithm is quite simple and efficient. Its computational cost scales logarithmically with beta Delta epsilon where beta is the inverse temperature and Delta epsilon is the width of the spectrum of the discretized Hamiltonian matrix.