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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
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | János Balog · Dennis le Plat |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2504.05932v2 (pdf) |
| Date submitted: | April 30, 2025, 8:28 a.m. |
| Submitted by: | Dennis le Plat |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| 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
Current status:
Reports on this Submission
Strengths
1- Opens new direction in low-energy integrable models; 2- Provides a recipe how to construct the nonperturbative series expansion of the moments of the rapidity distribution in the Lieb-Liniger model.
Weaknesses
1- For some readers a weakness is that the solution is rather involved; however in my opinion this should not be understood in negative context but as an inconvenience.
Report
Requested changes
1- Could the authors provide a physical understanding of exponentially suppressed terms in the ground-state energy, for example? It would be great if a parallel/comparison can be drawn with the findings of the paper of Marino https://doi.org/10.1088/1742-5468/ab4802 where the interpretation of the nonperturbative part is physical.
2- Typography: there is small inconsistency with dashes and hyphens: Lieb--Liniger vs Lieb-Liniger, Bose-Einstein, Coleman-Mermin-Wagner, etc. transseries vs trans-series.
Recommendation
Ask for minor revision