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We construct a coupled wire model for a sequence of non-Abelian quantum Hallstates occurring at filling factors $\nu=2/(2M+q)$ with integers $M$ andeven(odd) integers $q$ for fermionic(bosonic) states. They are termed $Z_2\times Z_2$ orbifold states, which have a topological order with a neutralsector 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 canbe viewed as two decoupled layers of Moore-Read (MR) state, whose neutralsector is described by the Ising $\times$ Ising CFT and contains a $Z_2 \timesZ_2$ fusion subalgebra. We demonstrate that orbifold states with $p>2$, alsocontaining a $Z_2 \times Z_2$ fusion algebra, can be obtained by couplingtogether an array of MR $\times$ MR wires through local interactions. Thecorresponding charge spectrum of quasiparticles is also examined. The orbifoldstates constructed here are complementary to the $Z_4$ orbifold states, whoseneutral edge theory is described by orbifold CFT with odd integer $p$ andcontains a $Z_4$ fusion algebra.

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