  We study hard-core bosons with unfrustrated nearest-neighbor hopping $t$ and
repulsive interaction $V$ on a zig-zag ladder. As a function of the boson
density $\rho$ and $V/t$, the ground state displays different quantum phases. A
standard one-component Tomonaga-Luttinger liquid is stable for $\rho<1/3$ (and
$\rho>2/3$) at any value of $V/t$. At commensurate densities $\rho=1/3$, $1/2$,
and $2/3$ insulating (crystalline) phases are stabilized for a sufficiently
large interaction $V$. For intermediate densities $1/3<\rho<2/3$ and large
$V/t$, the ground state shows a clear evidence of a bound state of two bosons,
implying gapped single-particle excitations but gapless excitations of boson
pairs. Here, the low-energy properties may be described by a two-component
Tomonaga-Luttinger liquid with a finite gap in the antisymmetric sector.
Finally, for the same range of boson densities and weak interactions, the
system is again a one-component Tomonaga-Luttinger liquid with no evidence of
any breaking of discrete symmetries, in contrast to the frustrated case, where
a ${\cal Z}_2$ symmetry breaking has been predicted.
