Continuum limit of a qubit-regularized SU(3) lattice gauge theory on a plaquette chain

arXiv:2603.01215v2 Announce Type: replace-cross Abstract: We show that a simple qubit-regularized $\mathrm{SU}(3)$ lattice gauge theory on a plaquette chain admits a continuum limit with massive gauge-invariant excitations, providing a minimal toy model of strong interactions without quarks. By mapping the plaquette-chain Hamiltonian to the three-state quantum clock model in a magnetic field, we demonstrate that the theory can be tuned to a continuum limit governed at short distances by the $\mathbb{Z}_3$ parafermion conformal field theory, which serves as the ultraviolet fixed point. A small relevant magnetic perturbation then drives the system to a massive continuum quantum field theory in the infrared, featuring relativistic particles. In this continuum theory we compute two universal ratios: the mass ratio of the lightest massive particles with opposite charge conjugation, $m^{-}/m^{+} = 1.459(2)$, and $\sqrt{\sigma}/m^{+} = 0.2648(2)$, where $\sigma$ denotes the string tension between a static quark and antiquark.

Abstract:We show that a simple qubit-regularized $\mathrm{SU}(3)$ lattice gauge theory on a plaquette chain admits a continuum limit with massive gauge-invariant excitations, providing a minimal toy model of strong interactions without quarks. By mapping the plaquette-chain Hamiltonian to the three-state quantum clock model in a magnetic field, we demonstrate that the theory can be tuned to a continuum limit governed at short distances by the $\mathbb{Z}_3$ parafermion conformal field theory, which serves as the ultraviolet fixed point. A small relevant magnetic perturbation then drives the system to a massive continuum quantum field theory in the infrared, featuring relativistic particles. In this continuum theory we compute two universal ratios: the mass ratio of the lightest massive particles with opposite charge conjugation, $m^{-}/m^{+} = 1.459(2)$, and $\sqrt{\sigma}/m^{+} = 0.2648(2)$, where $\sigma$ denotes the string tension between a static quark and antiquark.

Accepted for publication in Physical Review D. 7 pages of main text with 5 figures; 25 pages of Supplementary Material

High Energy Physics - Lattice (hep-lat); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th); Nuclear Theory (nucl-th); Quantum Physics (quant-ph)

arXiv:2603.01215 [hep-lat]

(or arXiv:2603.01215v2 [hep-lat] for this version)

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Continuum limit of a qubit-regularized SU(3) lattice gauge theory on a plaquette chain

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