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Exact Perturbative Results for the Lieb–Liniger and Gaudin–Yang Models

  • Marcos MariñoEmail author
  • Tomás Reis
Article
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Abstract

We present a systematic procedure to extract the perturbative series for the ground state energy density in the Lieb–Liniger and Gaudin–Yang models, starting from the Bethe ansatz solution. This makes it possible to calculate explicitly the coefficients of these series and to study their large order behavior. We find that both series diverge factorially and are not Borel summable. In the case of the Gaudin–Yang model, the first Borel singularity is determined by the non-perturbative energy gap. This provides a new perspective on the Cooper instability.

Keywords

Quantum gases Bethe ansatz Nonperturbative effects 

Notes

Acknowledgements

We would like to thank Sylvain Prolhac, Wilhelm Zwerger and specially Thierry Giamarchi and Félix Werner for useful discussions and comments on the manuscript. This work is supported in part by the Fonds National Suisse, subsidies 200021-156995 and 200020-141329, and by the NCCR 51NF40-141869 “The Mathematics of Physics” (SwissMAP).

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Département de Physique Théorique et Section de MathématiquesUniversité de GenèveGenevaSwitzerland

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