Numerical study of the chiral ${\mathbb{Z}}_3$ quantum phase transition in one spatial dimension

Abstract

Recent experiments on a one-dimensional chain of trapped alkali atoms [arXiv:1707.04344] have observed a quantum transition associated with the onset of period-3 ordering of pumped Rydberg states. This spontaneous ${\mathbb{Z}}_3$ symmetry breaking is described by a constrained model of hard-core bosons proposed by Fendley $etal.$ [arXiv:cond-mat/0309438]. By symmetry arguments, the transition is expected to be in the universality class of the ${\mathbb{Z}}_3$ chiral clock model with parameters preserving both time-reversal and spatial-inversion symmetries. We study the nature of the order-disorder transition in these models, and numerically calculate its critical exponents with exact diagonalization and density-matrix renormalization group techniques. We use finite-size scaling to determine the dynamical critical exponent $z$ and the correlation length exponent $\hat{I}½$. Our analysis presents the only known instance of a strongly-coupled transition between gapped states with $z\ne 1$, implying an underlying nonconformal critical field theory.

14 pages, 9 figures