Testing Variational Perturbation Theory for Effective Actions Using the Gaudin-Yang Model
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918143209766912 |
|---|---|
| author | Sharma, Pranav Furnstahl, R. J. |
| author_facet | Sharma, Pranav Furnstahl, R. J. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02919 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Testing Variational Perturbation Theory for Effective Actions Using the Gaudin-Yang Model Sharma, Pranav Furnstahl, R. J. Nuclear Theory Other Condensed Matter High Energy Physics - Phenomenology 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. |
| title | Testing Variational Perturbation Theory for Effective Actions Using the Gaudin-Yang Model |
| topic | Nuclear Theory Other Condensed Matter High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2506.02919 |