Self-Consistent RPA based on a Many-Body Vacuum

TL;DR

This paper extends Self-Consistent RPA to be compatible with a variational many-body vacuum, ensuring the Pauli principle is respected and demonstrating rapid convergence in a model case.

Contribution

It introduces a self-consistent RPA framework aligned with a variational fermionic vacuum, improving the theoretical foundation of RPA methods.

Findings

Pauli principle is fully respected in the extended RPA.

The correlation functions can be systematically expanded and converge rapidly.

The approach is demonstrated on a model case.

Abstract

Self-Consistent RPA is extended in a way so that it is compatable with a variational ansatz for the ground state wave function as a fermionic many-body vacuum. Employing the usual equation of motion technique, we arrive at extended RPA equations of the Self Consistent RPA structure. In principle the Pauli principle is, therefore, fully respected. However, the correlation functions entering the RPA matrix can only be obtained from a systematic expansion in powers of some combinations of RPA amplitudes. We demonstrate for a model case that this expansion may converge rapidly.