Asymptotic-freedom and massive glueballs in a qubit-regularized SU(2) gauge theory

Abstract

We argue that a simple qubit-regularized $\mathrm{SU}(2)$ lattice gauge theory (LGT) on a plaquette chain serves as a pseudo-one-dimensional toy model for Yang-Mills (YM) theory in three spatial dimensions. We map the chain Hamiltonian to the Transverse Field Ising Model (TFIM) in a uniform magnetic field and demonstrate that it can be tuned to a continuum limit in which the short-distance physics is governed by the asymptotically free Ising conformal field theory (CFT) describing free Majorana fermions, while the long-distance regime contains massive excitations of the $E_8$ quantum field theory (QFT) that can be interpreted as one-dimensional analogues of glueballs. Furthermore, we find $\sqrt{\sigma}/m_1 = 0.249(1)$ where $\sigma$ is the string tension between two static quarks and $m_1$ is the mass of the lightest glueball.