Parafermionic and decoupled multicritical points in a frustrated ${\mathbb{Z}}_6$ clock chain

Abstract

We introduce a generalised six-state clock chain that interpolates between the clock and Potts models via a multicritical point described by decoupled Ising and three-state Potts models. We find that this decoupling extends into stable phases that break only ${\mathbb{Z}}_2$ or ${\mathbb{Z}}_3$ symmetry. We also use boundary CFT analysis and level spectroscopy to conclusively identify a ${\mathbb{Z}}_6$ parafermion multicritical point terminating the clock model Luttinger-liquid phase. Our work shows that parafermions emerge far from integrability, even in systems with intertwined Ising and three-state Potts orders.