Combination of particle-particle and particle-hole renormalizations without double counting

Establish whether particle-particle ladder renormalizations and particle-hole-channel renormalizations of algebraic diagrammatic construction self-energy vertices can be combined without double counting, in the spirit of parquet approaches that treat multiple diagrammatic channels on an equal footing.

Background

The paper introduces EN partitioning as a particle-particle-channel renormalization through diagonal particle-particle ladder contributions, while related work dresses algebraic diagrammatic construction outer scattering vertices in the direct particle-hole channel using screened Coulomb interactions.

Combining these two types of renormalization could potentially incorporate complementary correlation effects, but the relevant diagrammatic contributions may overlap. The paper explicitly raises whether such a combination is possible and appropriate without double counting, identifying it as an unresolved question connected to parquet methodologies.