  A density-dependent gauge field may induce density-induced geometric
frustration, leading to a non-trivial interplay between density modulation and
frustration, which we illustrate for the particular case of ultra-cold bosons
in zig-zag optical lattices with a density-dependent hopping. We show that the
density-induced frustration leads in a rich landscape of quantum phases,
including Mott and bond-order insulators, two-component superfluids, chiral
superfluids, and partially-paired superfluids. We show as well that the
density-dependent hopping results in an effective repulsive or attractive
interactions, and that for the latter case the vacuum may be destabilized
leading to a strong compressibility. Finally, we discuss how the predicted
phases may be experimentally observed and characterized in time-of-flight
measurements using their characteristic signatures in the momentum
distribution.
