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
Highlights
The Lieb-Liniger model describes spinless bosons with contact interactions, whose motion is confined to one dimension [1]
We propose new conjectures about the groundstate energy of the Yang-Gaudin model, and discuss the radius of convergence of the partial resummations we perform
The one-dimensional quantum gas composed of N identical spinless point-like bosons of mass m with contact interactions, is described by the Lieb-Liniger Hamiltonian H which reads [1]
Summary
The Lieb-Liniger model describes spinless bosons with contact interactions, whose motion is confined to one dimension [1]. The exact ground-state energy can be obtained, in principle, from the exact Bethe Ansatz equations, only weak- and strong-coupling expansions are accessible to date [1, 40, 44,45,46,47,48,49,50,51].
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