Three roads to the energy gap

Abstract

We determine analytically the energy gap at weak coupling in the attractive multi-component Gaudin--Yang model, an integrable model which describes interacting fermions in one dimension with $\kappa$ components. We use three different methods. The first one is based on a direct analysis of the Bethe ansatz equations. The second method uses the theory of resurgence and the large order behavior of the perturbative series for the ground state energy. The third method is based on a renormalization group analysis. The three methods lead to the same answer, providing in this way a non-trivial test of the ideas of resurgence and renormalons as applied to non-relativistic many-body systems.

arXiv comment24 pages, 6 figures

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Cited by in corpus (3)

• The full analytic trans-series in integrable field theories
• Resurgence and renormalons in the one-dimensional Hubbard model
• All-order Resurgence from Complexified Path Integral in a Quantum Mechanical System with Integrability