## SciPost Submission Page

# Conjectures about the structure of strong- and weak-coupling expansions of a few ground-state observables in the Lieb-Liniger and Yang-Gaudin models

### by Guillaume Lang

### Submission summary

As Contributors: | Guillaume Lang |

Preprint link: | scipost_201908_00007v1 |

Date submitted: | 2019-08-09 |

Submitted by: | Lang, Guillaume |

Submitted to: | SciPost Physics |

Domain(s): | Theoretical |

Subject area: | Quantum Physics |

### Abstract

In this paper, we apply experimental number theory to two integrable quantum models in one dimension, the Lieb-Liniger Bose gas and the Yang-Gaudin Fermi gas with contact interactions. We identify patterns in weak- and strong-coupling series expansions of the ground-state energy, local correlation functions and pressure. Based on the most accurate data available in the literature, we make a few conjectures about their mathematical structure and extrapolate to higher orders.

###### Current status:

### Submission & Refereeing History

## Reports on this Submission

### Anonymous Report 1 on 2019-8-13 Invited Report

### Strengths

Important models. Attempt to relate integrability to number theory.

### Weaknesses

The author do not know that the most important in correlation functions is space

and time dependence.

The author do not know the literature on the subject.

### Report

1) The relation of integrability and number theory was explained in the paper

Quantum Correlations and Number Theory by H. E. Boos, V. E. Korepin, Y. Nishiyama, M. Shiroishi, Journal of Physics A Math. and General, vol 35, pages 4443-4452, 2002

2) Correlation functions were calculated in Lieb-Liniger model in the tex book

Quantum Inverse Scattering Method and Correlation Functions by V.E. Korepin, N.M. Bogoliubov and A.G. Izergin, Cambridge University Press , 1993.

### Requested changes

The author has to compare his results to the literature [see report] and resubmit the paper.