Resurgence and renormalons in the one-dimensional Hubbard model

TL;DR

This paper employs resurgent analysis to explore non-perturbative phenomena in the one-dimensional multicomponent Hubbard model, revealing renormalon singularities and providing explicit expressions for the energy gap, with exact solutions at half-filling.

Contribution

It introduces a resurgent framework to analyze non-perturbative effects in the Hubbard model and derives an explicit weak-coupling energy gap expression, including the full trans-series at half-filling.

Findings

Identification of renormalon-type Borel singularity linked to the energy gap.

Explicit next-to-leading order expression for the energy gap at weak coupling.

Exact trans-series and Stokes discontinuity for the half-filled case using Bethe ansatz.

Abstract

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. In the two-component, half-filled case, we use the Bethe ansatz solution to determine the full trans-series for the ground state energy, and the exact form of its Stokes discontinuity.