Testing variational perturbation theory for effective actions using the Gaudin-Yang model
Phys. Rev. C 112, 044309 – Published 14 October, 2025
DOI: https://doi.org/10.1103/tg2k-qg9v
Abstract
The background field formalism based on effective actions is a compelling framework for developing an effective field theory for nuclear density functional theory. Among the challenges in carrying out this development is handling both the particle-hole and pairing channels beyond the mean-field level, which includes how to incorporate collective degrees of freedom. Here we use the exactly solvable one-dimensional Gaudin-Yang model as a theoretical laboratory to explore candidate approaches. We compare variational perturbation theory (VPT) to ordinary many-body perturbation theory and the inversion method, all to second order in their respective expansions, and verify issues with Hubbard-Stratonovich auxiliary fields. VPT outperforms the other approaches at this level over a wide range of densities. The next steps to extend this approach toward nuclei are outlined.
