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 new algorithm is quite simple and efficient. Its computational cost scales logarithmically with $\beta\Delta\eps$ where $\beta$ is the inverse temperature, and $\Delta \eps$ is the width of the spectrum of the discretized Hamiltonian matrix. 
Lin Lin, Jianfeng Lu, Roberto Car and Weinan E