  Helical liquids have been experimentally detected in both nanowires and
ultracold atomic chains as the result of strong spin-orbit interactions. In
both cases the inner degrees of freedom can be considered as an additional
space dimension, providing an interpretation of these systems as synthetic
ladders, with artificial magnetic fluxes determined by the spin-orbit terms. In
this work, we characterize the helical state which appears at filling
$\nu=1/2$: this state is generated by a gap arising in the spin sector of the
corresponding Luttinger liquid and it can be interpreted as the one-dimensional
(1D) limit of a fractional quantum Hall state of bosonic pairs of fermions. We
study its main features, focusing on entanglement properties and correlation
functions. The techniques developed here provide a key example for the study of
similar quasi-1D systems beyond the semiclassical approximation commonly
adopted in the description of the Laughlin-like states.
