The Z₃ order–disorder quantum phase transition in the chiral clock model

The Z₃ chiral clock model describes a particular generalization of the transverse-field Ising model where each Ising spin is replaced by one with three states. Additionally, the interactions, which are invariant under Z₃-symmetry, are "chiral''. This model exhibits a second-order phase transition between an ordered phase, where the Z₃-symmetry is spontaneously broken, and a disordered phase. We study the nature of this transition and numerically calculate its critical exponents with the density-matrix renormalization group. In particular, we use finite-size scaling to determine the dynamical critical exponent z and the correlation length exponent ν. Our analysis presents one of the first nontrivial instances of a quantum phase transition with z ≠ 1, implying an underlying non-conformal critical field theory.