Building Symmetry Fractionalizations from a Bipartite Lattice Construction

We introduce a construction of symmetry-enriched topological phases on bipartite lattices in which two Z₂ spin liquids (SL) defined on the individual sublattices are combined. We demonstrate for a honeycomb lattice with spin-1/2 per site, where we can approach two different kinds of Z₂ SLs by condensing different anyon bound states. The first kind reproduces the known Z₂ SLs on the honeycomb lattice and makes explicit the fact that one can obtain a featureless ground state on the honeycomb lattice with spin-1/2 per site. The second kind gives a Z₂ SL with spinless excitations, which cannot be readily constructed from parton based approaches. We discuss generalizations to other bipartite lattices including a nonsymmorphic lattice and a lattice with magnetic translation symmetry.