Z2 topological liquid of hard-core bosons on a kagome lattice at 1/3 filling

We consider hard-core bosons on the kagome lattice in the presence of short range repulsive interactions and focus particularly on the filling factor 1/3. In the strongly interacting limit, the low energy excitations can be described by the quantum fully packed loop coverings on the triangular lattice. Using a combination of tensor-product state based methods and exact diagonalization techniques, we show that the system has an extended Z2 topological liquid phase as well as a lattice nematic phase. The latter breaks lattice rotational symmetry. By tuning appropriate parameters in the model, we study the quantum phase transition between the topological and the symmetry broken phases. We construct the critical theory for this transition using a mapping to an Ising gauge theory that predicts the transition to belong to the O(3) universality class.