Helical liquids have been experimentally detected in both
nanowires with strong spin-orbit coupling and
multi-component ultracold atomic chains with a
position-dependent coupling between the spin species. In
both cases the inner degree 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 the presence of interactions, non-trivial helical states
appear for special ratios of the particle density and the
synthetic magnetic flux, like in the two-dimensional
fractional quantum Hall regime.
In this talk, I characterize the helical state which appears
in a ladder model of repulsive ultracold fermions at filling
ν = 1/2: this state cannot be explained in terms of a simple
fermionic Laughlin-like analog; it is generated by a gap
arising in the spin sector of the corresponding Luttinger
liquid and it corresponds to a Laughlin state at filling 1/8
of bosonic pairs. I will discuss the techniques required for
its analytical description as well as its main features,
derived from a DMRG study.