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  • Letter
  • Open Access

Toward the continuum limit of a (1+1)D quantum link Schwinger model

Torsten V. Zache1,2,3, Maarten Van Damme4, Jad C. Halimeh5, Philipp Hauke5, and Debasish Banerjee6,7

  • 1Center for Quantum Physics, University of Innsbruck, 6020 Innsbruck, Austria
  • 2Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria
  • 3Heidelberg University, Institut für Theoretische Physik, Philosophenweg 16, 69120 Heidelberg, Germany
  • 4Department of Physics and Astronomy, University of Ghent, Krijgslaan 281, 9000 Gent, Belgium
  • 5INO-CNR BEC Center and Department of Physics, University of Trento, Via Sommarive 14, I-38123 Trento, Italy
  • 6Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhannagar, Kolkata 700064, India
  • 7Institut für Physik, Humboldt-Universität zu Berlin, Zum Großen Windkanal 6, 12489 Berlin, Germany

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Phys. Rev. D 106, L091502 – Published 3 November, 2022

DOI: https://doi.org/10.1103/PhysRevD.106.L091502

Abstract

The solution of gauge theories is one of the most promising applications of quantum technologies. Here, we discuss the approach to the continuum limit for U(1) gauge theories regularized via finite-dimensional Hilbert spaces of quantum spin-S operators, known as quantum link models. For quantum electrodynamics (QED) in one spatial dimension, we numerically demonstrate the continuum limit by extrapolating the ground state energy, the scalar, and the vector meson masses to large spin lengths S, large volume N, and vanishing lattice spacing a. By exactly solving Gauss’s law for arbitrary S, we obtain a generalized PXP spin model and count the physical Hilbert space dimension analytically. This allows us to quantify the required resources for reliable extrapolations to the continuum limit on quantum devices. We use a functional integral approach to relate the model with large values of half-integer spins to the physics at topological angle Θ=π. Our findings indicate that quantum devices will in the foreseeable future be able to quantitatively probe the QED regime with quantum link models.

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Phys. Rev. D 106, L091502– Published 3 November, 2022
  • Received 2 May 2021
  • Revised 14 March 2022
  • Accepted 7 October 2022
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