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We study the phases of hard-core-bosons on a two-dimensional periodichoneycomb lattice in the presence of an on-site potential with alternating signalong the different y-layers of the lattice. Using quantum Monte Carlosimulations supported by analytical calculations, we identify a weaktopological insulator, characterized by a zero Chern number but non-zero Berryphase, which is manifested at either density 1/4 or 3/4, as determined by thepotential pattern. Additionally, a charge-density-wave insulator is observed at1/2-filling, whereas the phase diagram at intermediate densities is occupied bya superfluid phase. The weak topological insulator is further shown to berobust against any amount of nearest-neighbor repulsion, as well as weaknext-nearest-neighbor repulsion. The experimental realization of our model isfeasible in an optical lattice setup.

Weak topological insulating phases of hard-core-bosons on the honeycomb lattice