Towards the continuum limit of a $(1+1)$d quantum link Schwinger model

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' 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 $\Theta =\pi$. Our findings indicate that quantum devices will in the foreseeable future be able to quantitatively probe the QED regime with quantum link models.

6+6 pages, 4+1 figures

References in corpus (13)

• Probing many-body dynamics on a 51-atom quantum simulator
• A universal qudit quantum processor with trapped ions
• Competing density-wave orders in a one-dimensional hard-boson model
• Optical Abelian Lattice Gauge Theories
• SU(2) hadrons on a quantum computer
• Towards Quantum Simulating QCD
• Quantum simulation of the Schwinger model: A study of feasibility
• Single qudit realization of the Deutsch algorithm using superconducting many-level quantum circuits
• Dynamics of the vacuum state in a periodically driven Rydberg chain
• Classically emulated digital quantum simulation for screening and confinement in the Schwinger model with a topological term
• Primitive Quantum Gates for Dihedral Gauge Theories
• Prospects for Simulating a Qudit Based Model of (1+1)d Scalar QED
• Truncation effects in the charge representation of the O(2) model

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