Efficient Numerical Self-consistent Mean-field Approach for Fermionic Many-body Systems by Polynomial Expansion on Spectral Density

TL;DR

This paper introduces a fast, scalable numerical algorithm using polynomial expansion to solve self-consistent Bogoliubov de Gennes equations for inhomogeneous superconductors, enabling efficient large-scale simulations.

Contribution

It presents a novel polynomial expansion method that improves computational efficiency and scalability for solving fermionic many-body systems in superconductivity.

Findings

Enhanced efficiency in large-scale parallel computations.

Successful application to vortex and junction problems.

Significant reduction in computational time.

Abstract

We propose an efficient numerical algorithm to solve Bogoliubov de Gennes equations self-consistently for inhomogeneous superconducting systems with a reformulated polynomial expansion scheme. This proposed method is applied to typical issues such as a vortex under randomly distributed impurities and a normal conducting junction sandwiched between superconductors. With various technical remarks, we show that its efficiency becomes remarkable in large-scale parallel performance.