Resurgence and renormalons in the one-dimensional Hubbard model
We use resurgent analysis to study non-perturbative aspects of the one-dimensional, multicomponent Hubbard model with an attractive interaction and arbitrary filling. In the two-component case, we show that the leading Borel singularity of the perturbative series for the ground-state energy is de...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SciPost
2022-11-01
|
| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.13.5.113 |
| _version_ | 1811308355535241216 |
|---|---|
| author | Marcos Mariño, Tomás Reis |
| author_facet | Marcos Mariño, Tomás Reis |
| author_sort | Marcos Mariño, Tomás Reis |
| collection | DOAJ |
| description | We use resurgent analysis to study non-perturbative aspects of the one-dimensional, multicomponent Hubbard model with an attractive interaction and arbitrary filling. In the two-component case, we show that the leading Borel singularity of the perturbative series for the ground-state energy is determined by the energy gap, as expected for superconducting systems. This singularity turns out to be of the renormalon type, and we identify a class of diagrams leading to the correct factorial growth. As a consequence of our analysis, we propose an explicit expression for the energy gap at weak coupling in the multi-component Hubbard model, at next-to-leading order in the coupling constant. In the two-component, half-filled case, we use the Bethe ansatz solution to determine the full trans-series for the ground state energy, and the exact form of its Stokes discontinuity. |
| first_indexed | 2024-04-13T09:21:43Z |
| format | Article |
| id | doaj.art-0277bb06521e489296aaa6b06079337a |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-04-13T09:21:43Z |
| publishDate | 2022-11-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-0277bb06521e489296aaa6b06079337a2022-12-22T02:52:33ZengSciPostSciPost Physics2542-46532022-11-0113511310.21468/SciPostPhys.13.5.113Resurgence and renormalons in the one-dimensional Hubbard modelMarcos Mariño, Tomás ReisWe use resurgent analysis to study non-perturbative aspects of the one-dimensional, multicomponent Hubbard model with an attractive interaction and arbitrary filling. In the two-component case, we show that the leading Borel singularity of the perturbative series for the ground-state energy is determined by the energy gap, as expected for superconducting systems. This singularity turns out to be of the renormalon type, and we identify a class of diagrams leading to the correct factorial growth. As a consequence of our analysis, we propose an explicit expression for the energy gap at weak coupling in the multi-component Hubbard model, at next-to-leading order in the coupling constant. In the two-component, half-filled case, we use the Bethe ansatz solution to determine the full trans-series for the ground state energy, and the exact form of its Stokes discontinuity.https://scipost.org/SciPostPhys.13.5.113 |
| spellingShingle | Marcos Mariño, Tomás Reis Resurgence and renormalons in the one-dimensional Hubbard model SciPost Physics |
| title | Resurgence and renormalons in the one-dimensional Hubbard model |
| title_full | Resurgence and renormalons in the one-dimensional Hubbard model |
| title_fullStr | Resurgence and renormalons in the one-dimensional Hubbard model |
| title_full_unstemmed | Resurgence and renormalons in the one-dimensional Hubbard model |
| title_short | Resurgence and renormalons in the one-dimensional Hubbard model |
| title_sort | resurgence and renormalons in the one dimensional hubbard model |
| url | https://scipost.org/SciPostPhys.13.5.113 |
| work_keys_str_mv | AT marcosmarinotomasreis resurgenceandrenormalonsintheonedimensionalhubbardmodel |