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

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.

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