Long-range entanglement and $\mathbb{Z}_2$ topological order of hardcore lattice bosons in the strong-interaction limit

We investigate long-range entanglement properties of a generic class of hardcore lattice boson models governed by two-body interactions. We propose a scenario to explain how $\mathbb{Z}_2$ topological order rises in the strong-interacting limit. We use a local unitary transformation which maps ground states of the original Hamiltonian to ground states of an exactly solvable model. The existence of $\mathbb{Z}_2$ topological order in the exactly solvable model is closely related to topological properties of a surface code. We study the topological ground state degeneracy and locally indistinguishability of ground states in the solvable model and demonstrate a relationship between the Z2 topological order of the original two-body interacting model and that of a four- or higher-than-four-body interacting model.