Multipole Representation of the Fermi Operator with Application to the Electronic Structure Analysis of Metallic Systems

TL;DR

This paper introduces a multipole representation of the Fermi-Dirac function to develop efficient algorithms for analyzing metallic systems' electronic structures, with computational costs scaling logarithmically with key parameters.

Contribution

It presents a novel multipole representation of the Fermi operator, enabling simple and efficient algorithms for electronic structure analysis of metals.

Findings

Computational cost scales logarithmically with inverse temperature and spectral width.

The method simplifies electronic structure calculations for metallic systems.

Demonstrates improved efficiency over previous approaches.

Abstract

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.