$\mathbb{Z}_4$ transitions in quantum loop models on a zig-zag ladder

TL;DR

This paper investigates quantum phase transitions from $ Z_4$ ordered phases in quantum loop models on a zig-zag ladder, revealing complex critical behaviors including Ising, Ashkin-Teller, and chiral transitions, and how model deformations influence these transitions.

Contribution

It uncovers the rich critical phenomena in quantum loop models on a zig-zag ladder and shows how model deformations can control the nature of phase transitions.

Findings

Identification of Ising and Ashkin-Teller critical points.

Discovery of an extended chiral transition interval.

Demonstration of transition change from continuous to first order via model deformation.

Abstract

We study the nature of quantum phase transitions out of $\mathbb{Z}_4$ ordered phases in quantum loop models on a zig-zag ladder. We report very rich critical behavior that includes a pair of Ising transitions, a multi-critical Ashkin-Teller point and a remarkably extended interval of a chiral transition. Although plaquette states turn out to be essential to realize chiral transitions, we demonstrate that critical regimes can be manipulated by deforming the model as to increase the presence of leg-dimerized states. This can be done to the point where the chiral transition turns into first order, we argue that this is associated with the emergence of a critical end point.