Numerical study of the chiral Z 3 quantum phase transition in one spatial dimension

摘要: Recent experiments on a one-dimensional chain of trapped alkali-metal atoms [Bernien et al., Nature (London) 551, 579 (2017)] have observed quantum transition associated with the onset period-3 ordering pumped Rydberg states. This spontaneous ${\mathbb{Z}}_{3}$ symmetry breaking is described by constrained model hard-core bosons proposed Fendley al. [Phys. Rev. B 69, 075106 (2004)]. By arguments, expected to be in universality class chiral clock parameters preserving both time-reversal and spatial-inversion symmetries. We study nature order--disorder these models numerically calculate its critical exponents exact diagonalization density-matrix renormalization-group techniques. use finite-size scaling determine dynamical exponent $z$ correlation length $\ensuremath{\nu}$. Our analysis presents only known instance strongly coupled generic between gapped states $z\ensuremath{\ne}1$, implying an underlying nonconformal critical-field theory.