Efficient numerical self-consistent mean-field approach for fermionic many-body systems by polynomial expansion on spectral density

Nagai, Yuki   ; Ota, Yukihiro*; Machida, Masahiko  

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.