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Resurgence and renormalons in the one-dimensional Hubbard model

by Marcos Marino, Tomas Reis

Submission summary

As Contributors: Tomas Reis
Arxiv Link: (pdf)
Date submitted: 2021-11-18 17:40
Submitted by: Reis, Tomas
Submitted to: SciPost Physics
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.

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Submission & Refereeing History

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Resubmission 2006.05131v3 on 18 November 2021

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Tomas Reis  on 2022-01-07  [id 2076]

We would like to thank the referee for their attentive reading of our manuscript. We have incorporated all the suggestions in this revision of the paper, and included the requested clarifications.

Perhaps we can comment more particularly on point (9) raised by the referee. In trans-series arising from ordinary differential equations, the trans-series parameters are all related, and for equations of first order, the coefficient of the \ell-th “instanton" correction is indeed of the form C^\ell. However, in trans-series appearing in QFT, we do not have any reason to believe that this will be also the case (or at least we are not aware of any result going into that direction). That’s why we have decided to write a more generic trans-series form.

The point (11) has been also addressed. It turns out that all the series appearing in the trans-series (except the perturbative one) are Borel summable along the positive real axis, so the median resummation is much simplified.