Resurgence and renormalons in the one-dimensional Hubbard model

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.

arXiv comment37 pages, 4 figures, v3: minor clarifications and corrections

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• The full analytic trans-series in integrable field theories
• Analytic resurgence in the O(4) model
• Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ${\varphi }^3$ QFT in 6 Dimensions
• Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED
• All-order Resurgence from Complexified Path Integral in a Quantum Mechanical System with Integrability
• Resurgence and $1/N$ Expansion in Integrable Field Theories
• Capturing the cascade: a transseries approach to delayed bifurcations
• Resurgence in the Scalar Quantum Electrodynamics Euler-Heisenberg Lagrangian
• Love--Lieb integral equations: applications, theory, approximations, and computation