Density-induced geometric frustration of ultra-cold bosons in optical lattices

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.