Ising versus $SU(2)_2$ string-net ladder

TL;DR

This paper investigates the competition between two non-Abelian quantum phases derived from $SU(2)_2$ string-net models on a ladder, revealing a critical point described by $so(2)_1$ conformal field theory.

Contribution

It identifies the low-energy sector of the $SU(2)_2$ string-net ladder as equivalent to the transverse-field cluster model, providing insight into the phase structure.

Findings

The low-energy sector maps to the transverse-field cluster model.

A critical point is characterized by $so(2)_1$ conformal field theory.

Other sectors are understood by freezing spins in the model.

Abstract

We consider the string-net model obtained from $SU(2)_2$ fusion rules. These fusion rules are shared by two different sets of anyon theories. In this work, we study the competition between the two corresponding non-Abelian quantum phases in the ladder geometry. A detailed symmetry analysis shows that the nontrivial low-energy sector corresponds to the transverse-field cluster model that displays a critical point described by the $so(2)_1$ conformal field theory. Other sectors are obtained by freezing spins in this model.