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

Year: 2022

Authors: Zache TV., Van Damme M., Halimeh JC., Hauke P., Banerjee D.

Autors Affiliation: Univ Innsbruck, Ctr Quantum Phys, A-6020 Innsbruck, Austria; Austrian Acad Sci, Inst Quantum Opt & Quantum Informat, A-6020 Innsbruck, Austria; Heidelberg Univ, Inst Theoret Phys, Philosophenweg 16, D-69120 Heidelberg, Germany; Univ Ghent, Dept Phys & Astron, Krijgslaan 281, B-9000 Ghent, Belgium; Univ Trento, CNR, INO, BEC Ctr, Via Sommar 14, I-38123 Trento, Italy; Univ Trento, Dept Phys, Via Sommar 14, I-38123 Trento, Italy; HBNI, Saha Inst Nucl Phys, 1-AF Bidhannagar, Kolkata 700064, India; Humboldt Univ, Inst Phys, Zum Grossen Windkanal 6, D-12489 Berlin, Germany.

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 Theta 1/4 pi. Our findings indicate that quantum devices will in the foreseeable future be able to quantitatively probe the QED regime with quantum link models.

Journal/Review: PHYSICAL REVIEW D

Volume: 106 (9)      Pages from: L091502-1  to: L091502-8

More Information: We thank Shailesh Chandrasekharan, Robert Ott, Arnab Sen, and Uwe-Jens Wiese for useful discussions. This work was supported by the Simons Collaboration on UltraQuantum Matter, which is a grant from the Simons Foundation (651440, P. Z.). D. B. acknowledges support by the German Research Foundation (D FG), Grant No. BA 5847/2-1 and DFG Project No. 392051989. This work is part of and supported by the Interdisciplinary Center Q@TN-Quantum Science and Technologies at Trento, the DFG Collaborative Research Centre SFB 1225 (ISOQUANT), the Provincia Autonoma di Trento, and the ERC Starting Grant No. StrEnQTh (Project No. 804305).
KeyWords: Gauge-invariance; Simulations; Realization; Dynamics
DOI: 10.1103/PhysRevD.106.L091502

Citations: 20
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