Many-body perturbation theory for strongly correlated effective Hamiltonians using effective field theory methods
Introducing low-energy effective Hamiltonians is usual to grasp most correlations in quantum many-body problems. For instance, such effective Hamiltonians can be treated at the mean-field level to reproduce some physical properties of interest. Employing effective Hamiltonians that contain many-body...
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2025-01-01
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| author | Raphaël Photopoulos, Antoine Boulet |
| author_facet | Raphaël Photopoulos, Antoine Boulet |
| author_sort | Raphaël Photopoulos, Antoine Boulet |
| collection | DOAJ |
| description | Introducing low-energy effective Hamiltonians is usual to grasp most correlations in quantum many-body problems. For instance, such effective Hamiltonians can be treated at the mean-field level to reproduce some physical properties of interest. Employing effective Hamiltonians that contain many-body correlations renders the use of perturbative many-body techniques difficult because of the overcounting of correlations. In this work, we develop a strategy to apply an extension of the many-body perturbation theory starting from an effective interaction that contains correlations beyond the mean-field level. The goal is to re-organize the many-body calculation to avoid the overcounting of correlations originating from the introduction of correlated effective Hamiltonians in the description. For this purpose, we generalize the formulation of the Rayleigh-Schrödinger perturbation theory by including free parameters adjusted to reproduce the appropriate limits. In particular, the expansion in the bare weak-coupling regime and the strong-coupling limit serves as a valuable input to fix the value of the free parameters appearing in the resulting expression. This method avoids double counting of correlations using beyond-mean-field strategies for the description of many-body systems. The ground state energy of various systems relevant for ultracold atomic, nuclear, and condensed matter physics is reproduced qualitatively beyond the domain of validity of the standard many-body perturbation theory. Finally, our method suggests interpreting the formal results obtained as an effective field theory using the proposed reorganization of the many-body calculation. The results, like ground state energies, are improved systematically by considering higher orders in the extended many-body perturbation theory while maintaining a straightforward polynomial expansion. |
| format | Article |
| id | doaj-art-80d52367c94945f2ab052a96678751d2 |
| institution | Kabale University |
| issn | 2542-4653 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SciPost |
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| spelling | doaj-art-80d52367c94945f2ab052a96678751d22025-01-06T16:39:39ZengSciPostSciPost Physics2542-46532025-01-0118100310.21468/SciPostPhys.18.1.003Many-body perturbation theory for strongly correlated effective Hamiltonians using effective field theory methodsRaphaël Photopoulos, Antoine BouletIntroducing low-energy effective Hamiltonians is usual to grasp most correlations in quantum many-body problems. For instance, such effective Hamiltonians can be treated at the mean-field level to reproduce some physical properties of interest. Employing effective Hamiltonians that contain many-body correlations renders the use of perturbative many-body techniques difficult because of the overcounting of correlations. In this work, we develop a strategy to apply an extension of the many-body perturbation theory starting from an effective interaction that contains correlations beyond the mean-field level. The goal is to re-organize the many-body calculation to avoid the overcounting of correlations originating from the introduction of correlated effective Hamiltonians in the description. For this purpose, we generalize the formulation of the Rayleigh-Schrödinger perturbation theory by including free parameters adjusted to reproduce the appropriate limits. In particular, the expansion in the bare weak-coupling regime and the strong-coupling limit serves as a valuable input to fix the value of the free parameters appearing in the resulting expression. This method avoids double counting of correlations using beyond-mean-field strategies for the description of many-body systems. The ground state energy of various systems relevant for ultracold atomic, nuclear, and condensed matter physics is reproduced qualitatively beyond the domain of validity of the standard many-body perturbation theory. Finally, our method suggests interpreting the formal results obtained as an effective field theory using the proposed reorganization of the many-body calculation. The results, like ground state energies, are improved systematically by considering higher orders in the extended many-body perturbation theory while maintaining a straightforward polynomial expansion.https://scipost.org/SciPostPhys.18.1.003 |
| spellingShingle | Raphaël Photopoulos, Antoine Boulet Many-body perturbation theory for strongly correlated effective Hamiltonians using effective field theory methods SciPost Physics |
| title | Many-body perturbation theory for strongly correlated effective Hamiltonians using effective field theory methods |
| title_full | Many-body perturbation theory for strongly correlated effective Hamiltonians using effective field theory methods |
| title_fullStr | Many-body perturbation theory for strongly correlated effective Hamiltonians using effective field theory methods |
| title_full_unstemmed | Many-body perturbation theory for strongly correlated effective Hamiltonians using effective field theory methods |
| title_short | Many-body perturbation theory for strongly correlated effective Hamiltonians using effective field theory methods |
| title_sort | many body perturbation theory for strongly correlated effective hamiltonians using effective field theory methods |
| url | https://scipost.org/SciPostPhys.18.1.003 |
| work_keys_str_mv | AT raphaelphotopoulosantoineboulet manybodyperturbationtheoryforstronglycorrelatedeffectivehamiltoniansusingeffectivefieldtheorymethods |