A partial fraction decomposition of the Fermi function

TL;DR

The paper introduces a partial fraction decomposition of the Fermi function that converges faster than traditional methods, enabling more efficient calculations in electronic structure and transport theories.

Contribution

It presents a novel partial fraction decomposition of the Fermi function with superior convergence properties compared to the Matsubara expansion.

Findings

Fermi function decomposed into a finite sum over simple poles

Decomposition converges faster than exponential in a well-defined region

Enhances computational efficiency in electronic structure calculations

Abstract

A partial fraction decomposition of the Fermi function resulting in a finite sum over simple poles is proposed. This allows for efficient calculations involving the Fermi function in various contexts of electronic structure or electron transport theories. The proposed decomposition converges in a well-defined region faster than exponential and is thus superior to the standard Matsubara expansion.