U(1) Emergence versus Chiral Symmetry Restoration in the Ashkin Teller Model

TL;DR

This paper investigates how vortex suppression in the Ashkin Teller model leads to distinct phase transitions and symmetry enhancements, revealing the role of topological defects in symmetry phenomena.

Contribution

It demonstrates the emergence of U(1) symmetry through vortex suppression and the replacement of this phase by chiral symmetry restoration when non-chiral vortices are suppressed.

Findings

Suppression of vortices splits the transition and creates an intermediate U(1) phase.

Selective vortex suppression can restore chiral symmetry.

The phenomena extend to all even $ abla_n$ ferromagnets.

Abstract

We show that suppression of vortices in the Ashkin Teller ferromagnet on a square lattice splits the order-disorder transition and opens up an intermediate phase where the macroscopic symmetry enhances to U(1). When we selectively suppress the formation of non-chiral vortices, chiral vortices proliferate and replace the U(1) phase with a new phase where chiral symmetry is restored. This result demonstrates a fascinating phenomenon in which the symmetry information encoded in topological defects manifests itself in the symmetry of the phase where the defects proliferate. We also show that this phenomenon can occur in all $\mathbb{Z}_n$ ferromagnets with even values of $n$.