Towards a frequency independent incremental ab initio scheme for the self energy

TL;DR

This paper introduces a frequency independent formulation for calculating the self energy in many-body problems, enabling faster and equally accurate correlation calculations for large systems.

Contribution

A novel frequency independent approach for self energy calculation is developed, matching the accuracy of traditional methods while significantly improving computational efficiency.

Findings

Achieves exact numerical results as frequency dependent schemes

Provides a 50-fold speed-up in calculations

Successfully applied to a realistic molecular system

Abstract

The frequency dependence of the self energy of a general many--body problem is identified as a main obstacle in correlation calculations based on local approaches. A frequency independent formulation is proposed instead and proven to yield exactly the same numerical results as the original common scheme. Our approach is embedded in a general local-orbital based ab initio frame to obtain the Green's function for large heterogenous systems. First a Green's function formalism is introduced. Then the self energy is constructed from an incremental scheme. Subsequently we apply the proposed frequency independent formulation. The theory is applied to para-ditholbenzene as a realistic system and the numerical accuracy of the correlation contributions obtained from our frequency independent access are carefully tested against the exact frequency dependent results. Perfect agreement is reached and a speed--up of a factor 50 is established for the incremental scheme.