Coupled Wire Model of $Z_2 \times Z_2$ Orbifold Quantum Hall States

TL;DR

This paper develops a coupled wire model for non-Abelian $Z_2 imes Z_2$ orbifold quantum Hall states, revealing their topological order, fusion algebra, and quasiparticle spectrum, extending understanding of complex quantum Hall phases.

Contribution

It introduces a coupled wire construction for $Z_2 imes Z_2$ orbifold states with novel topological and fusion properties, generalizing previous models and connecting to orbifold conformal field theories.

Findings

Constructed coupled wire models for $Z_2 imes Z_2$ orbifold states.

Analyzed the topological order and fusion algebra of these states.

Examined the quasiparticle charge spectrum.

Abstract

We construct a coupled wire model for a sequence of non-Abelian quantum Hall states occurring at filling factors $\nu=2/(2M+q)$ with integers $M$ and even(odd) integers $q$ for fermionic(bosonic) states. They are termed $Z_2 \times Z_2$ orbifold states, which have a topological order with a neutral sector described by the $c=1$ orbifold conformal field theory (CFT) at radius $R_{\rm orbifold}=\sqrt{p/2}$ with even integers $p$. When $p=2$, the state can be viewed as two decoupled layers of Moore-Read (MR) state, whose neutral sector is described by the Ising $\times$ Ising CFT and contains a $Z_2 \times Z_2$ fusion subalgebra. We demonstrate that orbifold states with $p>2$, also containing a $Z_2 \times Z_2$ fusion algebra, can be obtained by coupling together an array of MR $\times$ MR wires through local interactions. The corresponding charge spectrum of quasiparticles is also examined. The orbifold states constructed here are complementary to the $Z_4$ orbifold states, whose neutral edge theory is described by orbifold CFT with odd integer $p$ and contains a $Z_4$ fusion algebra.