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Resurgence and renormalons in the one-dimensional Hubbard model

by Marcos Marino, Tomas Reis

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Tomas Reis
Submission information
Preprint Link: scipost_202209_00039v1  (pdf)
Date accepted: 2022-09-23
Date submitted: 2022-09-19 15:07
Submitted by: Reis, Tomas
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
  • Mathematical Physics
Approach: Theoretical


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.

Author comments upon resubmission

We thank the referee for their comments and feedback. We have incorporated both requested changes.

List of changes

(1) We expanded the caption of Figure 1 to include an explanation of the full and dashed lines.

(2) We added some lines to the paragraph preceeding equation 2.23 in which we comment on other contributions to 2.14. We also expanded the text before equation 2.27.

Published as SciPost Phys. 13, 113 (2022)

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