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

TL;DR

This paper explores a generalized six-state clock chain that reveals multicritical points with decoupled Ising and Potts models, demonstrating parafermion emergence beyond integrability.

Contribution

It introduces a model interpolating between clock and Potts models, identifying a $ Z_6$ parafermion multicritical point using boundary CFT and level spectroscopy.

Findings

Decoupling extends into phases breaking $ Z_2$ or $ Z_3$ symmetry.

Identifies a $ Z_6$ parafermion multicritical point.

Parafermions emerge far from integrability.

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.