Journal
JOURNAL OF STATISTICAL PHYSICS
Volume 177, Issue 6, Pages 1148-1156Publisher
SPRINGER
DOI: 10.1007/s10955-019-02413-1
Keywords
Quantum gases; Bethe ansatz; Nonperturbative effects
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Funding
- Fonds National Suisse [200021-156995, 200020-141329]
- NCCR [51NF40-141869]
- Swiss National Science Foundation (SNF) [200021_156995] Funding Source: Swiss National Science Foundation (SNF)
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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.
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