Resurgence and renormalons in the one-dimensional Hubbard model

Understand

We use resurgent analysis to study non-perturbative aspects of the one-dimensional, multicomponent Hubbard model with an attractive interaction and arbitrary filling.

• In the two-component case, we show that the leading Borel singularity of the perturbative series for the ground-state energy is determined by the energy gap, as expected for superconducting systems.
• This singularity turns out to be of the renormalon type, and we identify a class of diagrams leading to the correct factorial growth.
• As a consequence of our analysis, we propose an explicit expression for the energy gap at weak coupling in the multi-component Hubbard model, at next-to-leading order in the coupling constant.