Critical Exponents of the Chiral Potts Model from Conformal Field Theory

TL;DR

This paper uses conformal field theory to analyze the critical behavior of the Z_N-invariant chiral Potts model, deriving critical exponents and revealing novel symmetries and conserved charges.

Contribution

It provides a conformal field theory framework for the chiral Potts model, connecting lattice results with continuum symmetries and conserved quantities.

Findings

Critical exponents match exact lattice results.

Identification of a novel space-time symmetry.

Existence of infinite conserved charges on the self-dual line.

Abstract

The $Z_N$-invariant chiral Potts model is considered as a perturbation of a $Z_N$ conformal field theory. In the self-dual case the renormalization group equations become simple, and yield critical exponents and anisotropic scaling which agree with exact results for the super-integrable lattice models. Although the continuum theory is not Lorentz invariant, it respects a novel type of space-time symmetry which allows for the observed spontaneous breaking of translational symmetry in the ground state. The continuum theory is shown to possess an infinite number of conserved charges on the self-dual line, which remain conserved when the theory is perturbed by the energy operator.