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

## TL;DR

This paper explores the mathematical structure of series expansions in two integrable quantum models, using experimental number theory to identify patterns and make conjectures about their behavior at different coupling strengths.

## Contribution

It introduces conjectures about the structure of weak- and strong-coupling expansions in the Lieb-Liniger and Yang-Gaudin models based on empirical data.

## Key findings

- Identified patterns in series expansions of ground-state observables.
- Formulated conjectures on the mathematical structure of these expansions.
- Provided extrapolations to higher orders based on data.

## 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.