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Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution

by Guillaume Lang, Frank Hekking, Anna Minguzzi

Submission summary

As Contributors: Guillaume Lang · Anna Minguzzi
Arxiv Link: (pdf)
Date submitted: 2017-06-22 02:00
Submitted by: Lang, Guillaume
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
Approach: Theoretical


We study the ground-state properties and excitation spectrum of the Lieb-Liniger model, i.e. the one-dimensional Bose gas with repulsive contact interactions. We solve the Bethe-Ansatz equations in the thermodynamic limit by using an analytic method based on a series expansion on orthogonal polynomials developed in \cite{Ristivojevic} and push the expansion to an unprecedented order. By a careful analysis of the mathematical structure of the series expansion, we make a conjecture for the analytic exact result at zero temperature and show that the partially resummed expressions thereby obtained compete with accurate numerical calculations. This allows us to evaluate the density of quasi-momenta, the ground-state energy, the local two-body correlation function and Tan's contact. Then, we study the two branches of the excitation spectrum. Using a general analysis of their properties and symmetries, we obtain novel analytical expressions at arbitrary interaction strength which are found to be extremely accurate in a wide range of intermediate to strong interactions.

Ontology / Topics

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Bethe Ansatz Exactly solvable models Lieb-Liniger model One-dimensional Bose gas Orthogonal polynomials Tan contact

Published as SciPost Phys. 3, 003 (2017)

Author comments upon resubmission

List of changes

- The conclusion has been modified to include a summary
- Typos noted by the referees have been corrected
- arXiv references published inbetween have been actuated

Reports on this Submission

Anonymous Report 1 on 2017-6-22 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:1609.08865v3, delivered 2017-06-22, doi: 10.21468/SciPost.Report.173


1) The paper is well written, and the results are presented clearly
2) The material is well contextualized, thanks to a large number of references and discussions on the existing literature
3) Many analytical results are presented in a unified way


No weaknesses


The authors have addressed all of my comments and questions. I now recommend the manuscript for publication.

Requested changes

No requested changes

  • validity: -
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  • formatting: excellent
  • grammar: excellent

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