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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: https://arxiv.org/abs/2006.05131v3 (pdf)
Date submitted: 2021-11-18 17:40
Submitted by: Reis, Tomas
Submitted to: SciPost Physics
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
  • Mathematical Physics
Approach: Theoretical

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.

Current status:
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Resubmission 2006.05131v3 on 18 November 2021

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