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The complete trans-series for conserved charges in the Lieb-Liniger model
by Zoltán Bajnok, János Balog, Ramon Miravitllas, Dennis le Plat, István Vona
Submission summary
| Authors (as registered SciPost users): | János Balog · Dennis le Plat |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202509_00022v1 (pdf) |
| Date submitted: | Sept. 10, 2025, 9:01 a.m. |
| Submitted by: | Dennis le Plat |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We determine the complete trans-series solution for the (non-relativistic) moments of the rapidity density in the Lieb-Liniger model. The trans-series is written explicitly in terms of a perturbative basis, which can be obtained from the already known perturbative expansion of the density by solving several ordinary differential equations. Unknown integration constants are fixed from Volin's method. We have checked that our solution satisfies the analytical consistency requirements including the newly derived resurgence relations and agrees with the high precision numerical solution. Our results also provides the full analytic trans-series for the capacitance of the coaxial circular plate capacitor.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
In particular the referee suggested to provide a physical understanding of the non-perturbative corrections. In response to this request, we added a paragraph in the conclusions of the paper. Though it is natural to ask, whether results from the closely related Gaudin-Yang model can aid in gaining physical insight, the situation differs for the Lieb-Liniger model in several aspects. Most prominently, these include the repulsive nature of the interactions and the continuous excitation spectrum. In the paragraph added, we discuss how the non-perturbative corrections likely originate from renormalon effects rather than semiclassical mechanisms.
A complete physical interpretation remains an open and challenging question. We believe that this question deserves some deeper investigation on its own and aim to return to it in subsequent work.
We have also corrected several typographical inconsistencies throughout the manuscript.
List of changes
- added discussion on physical understanding of exponentially suppressed terms in the conclusions.
- Added reference (new [38])
- correction of several typographical inconsistencies
Current status:
Reports on this Submission
Strengths
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Develop a method which systematically compute the exact tran-series result of higher conserved charges of Lieb-Liniger model.
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The exact tran-series result for the charges is obtained for the first time.
Weaknesses
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The paper is quite technical, more efforts is needed to make it more pedagogical.
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The physical implications of the non-perturbative contributions is unclear.
Report
This paper presents new progress in the study of the Lieb-Liniger model by developing a systematic method to compute the analytic trans-series for its higher conserved charges. The authors extend methods previously developed for relativistic QFTs to this non-relativistic integrable system. The work is technically sound, the results are solid, and they have the potential for generalization to other integrable models and the computation of further observables. The manuscript is well-structured but highly technical. I have only two comments.
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The paper is quite technical. While this is understandable to a certain extent, it would be beneficial if the authors made a greater effort to make the paper more pedagogical, especially for readers who are not familiar with their previous work. For example, before delving into the details, the authors could devote a paragraph or two to outlining the main steps of the computation, or even provide a figure illustrating the procedure if possible. A short appendix explaining Volin's method in the current context would also be helpful.
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My second comment concerns the physical relevance of the results. To strengthen the paper's impact, it would be very helpful if the authors could discuss the physical implications of their findings. The physical origin of the non-perturbative contributions (such as renormalons or instantons) they obtain is not entirely clear at this stage, though the authors do mention some possible explanations. Another aspect is whether these non-perturbative corrections could be observed experimentally, given that the Lieb-Liniger model can be realized in cold atom experiments. It would be valuable if the authors could also provide comments on this point.
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