  We consider a one-dimensional "zigzag" lattice, pictured as a two-site wide
single strip taken from a triangular lattice, affected by a tunable homogeneous
magnetic flux piercing its triangular plaquettes. We focus on a semi-synthetic
lattice produced by combining a one-dimensional spin-dependent lattice in the
long direction with laser-induced transitions between atomic internal states
that define the short synthetic dimension. In contrast to previous studies on
semi-synthetic lattices, the atom-atom interactions are nonlocal in both
lattice directions. We investigate the ground-state properties of the system
for the case of strongly interacting bosons, and find that the interplay
between the frustration induced by the magnetic field and the interactions
gives rise to an exotic gapped phase at fractional filling factors
corresponding to one particle per magnetic unit cell.
