  We introduce a coupled wire model for a sequence of non-Abelian quantum Hall
states that generalize the Z4 parafermion Read Rezayi state. The Z4 orbifold
quantum Hall states occur at filling factors \nu = 2/(2m-p) for odd integers
$m$ and $p$, and have a topological order with a neutral sector characterized
by the orbifold conformal field theory with central charge $c=1$ at radius
$R=\sqrt{p/2}$. When $p=1$ the state is Abelian. The state with $p=3$ is the
$Z_4$ Read Rezayi state, and the series of $p\ge 3$ defines a sequence of
non-Abelian states that resembles the Laughlin sequence. Our model is based on
clustering of electrons in groups of four, and is formulated as a two fluid
model in which each wire exhibits two phases: a weak clustered phase, where
charge $e$ electrons coexist with charge $4e$ bosons and a strong clustered
phase where the electrons are strongly bound in groups of 4. The transition
between these two phases on a wire is mapped to the critical point of the 4
state clock model, which in turn is described by the orbifold conformal field
theory. For an array of wires coupled in the presence of a perpendicular
magnetic field, strongly clustered wires form a charge $4e$ bosonic Laughlin
state with a chiral charge mode at the edge, but no neutral mode and a gap for
single electrons. Coupled wires near the critical state form quantum Hall
states with a gapless neutral mode described by the orbifold theory. The
coupled wire approach allows us to employ the Abelian bosonization technique to
fully analyze the physics of single wire, and then to extract most topological
properties of the resulting non-Abelian quantum Hall states. These include the
list of quasiparticles, their fusion rules, the correspondence between bulk
quasiparticles and edge topological sectors, and most of the phases associated
with quasiparticles winding one another.
