RPA stands for the random phase approximation is often used as synonym for the adiabatic connection fluctuation dissipation theorem (ACFDT). RPA/ACFDT provides access to the correlation energy of a system and can be understood in terms of Feynman diagrams as an infinite sum of all bubble diagrams, where excitonic effects (interactions between electrons and holes) are neglected. The RPA/ACFDT is used as a post-processing tool to determine a more accurate groundstate energy.
The following page contains more information about the theory behind RPA/ACFDT:
A practical guide to ACFDT/RPA calculations can be found on following here.