Z₂ Topological Quantum Paramagnet on a honeycomb bilayer

Topological quantum paramagnets are exotic states of matter with trivial paramagnetic ground states hosting topological excitations. Here we show that a simple model of quantum spins on a honeycomb bilayer hosts a Z₂ topological quantum paramagnet in the presence of spin-orbit coupling. The Z₂ invariant is the same as that in the case of the fermionic quantum spin Hall state. We further show that upon making one of the Heisenberg couplings stronger the system undergoes a topological quantum phase transition, where the Z₂ invariant vanishes, to a different topological quantum paramagnet. In this case the edge states are disconnected from the bulk excitations. This phase is characterized by a different topological invariant. This physics is amenable to experiments, where an anisotropic coupling can be induced under pressure.