  We study spinless electrons in a single channel quantum wire interacting
through attractive interaction, and the quantum Hall states that may be
constructed by an array of such wires. For a single wire the electrons may form
two phases, the Luttinger liquid and the strongly paired phase. The Luttinger
liquid is gapless to one- and two-electron excitations, while the strongly
paired state is gapped to the former and gapless to the latter. In contrast to
the case in which the wire is proximity-coupled to an external superconductor,
for an isolated wire there is no separate phase of a topological, weakly
paired, superconductor. Rather, this phase is adiabatically connected to the
Luttinger liquid phase. The properties of the one dimensional topological
superconductor emerge when the number of channels in the wire becomes large.
The quantum Hall states that may be formed by an array of single-channel wires
depend on the Landau level filling factors. For odd-denominator fillings
$\nu=1/(2n+1)$, wires at the Luttinger phase form Laughlin states while wires
in the strongly paired phase form bosonic fractional quantum Hall state of
strongly-bound pairs at a filling of $1/(8n+4)$. The transition between the two
is of the universality class of Ising transitions in three dimensions. For
even-denominator fractions $\nu=1/2n$ the two single-wire phases translate into
four quantum Hall states. Two of those states are bosonic fractional quantum
Hall states of weakly- and strongly- bound pairs of electrons. The other two
are non-Abelian quantum Hall states, which originate from coupling wires close
to their critical point. One of these non-Abelian states is the Moore-Read
state. The transition between all these states are of the universality class of
Majorana transitions. We point out some of the properties that characterize the
different phases and the phase transitions.
