Interacting bosons in generalized zig-zag and railroad-trestle models

We theoretically study the ground-state phase diagram of strongly interacting bosons on a generalized zig-zag ladder model, the rail-road trestle (RRT) model. By means of analytical arguments in the limits of decoupled chains and the case of vanishing fillings as well as extensive DMRG calculations we examine the rich interplay between frustration and interaction for various parameter regimes. We distinguish three different cases, the fully frustrated RRT model where the dispersion relation becomes doubly degenerate and an extensive chiral superfluid regime is found, the anti-symmetric RRT with alternating $\pi$ and $0$ fluxes through the ladder plaquettes and the sawtooth limit, which is closely related to the latter case. We study detailed phase diagrams which include besides different single component superfluids, the chiral superfluid phases, the two component superfluids and different gaped phases, with dimer and a charge-density wave order.