Phase diagram of hard-core bosons on a zig-zag ladder

We study hard-core bosons with unfrustrated nearest-neighbor hopping t and repulsive interaction V on a zigzag ladder. As a function of the boson density ρ and V/t, the ground state displays different quantum phases. A standard one-component Tomonaga-Luttinger liquid is stable for ρ<1/3 (and ρ>2/3) at any value of V/t. At commensurate densities ρ=1/3, 1/2, and 2/3 insulating (crystalline) phases are stabilized for a sufficiently large interaction V. For intermediate densities 1/3<ρ<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. These properties can be understood by the fact that the antisymmetric sector acquires a gap and a single gapless mode survives. 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 Z2 symmetry breaking has been predicted.