Toric code and stabilizers
Local commuting operators can produce a globally entangled ground space.
$$H=-J_e\sum_s A_s-J_m\sum_p B_p$$
What this means
Local commuting operators can produce a globally entangled ground space.
Deep dive: mathematical and physical mechanism
On a square lattice with qubits on edges, star operators $A_s$ multiply $X$ on incident edges and plaquette operators $B_p$ multiply $Z$ around a face. On a torus, two independent noncontractible Wilson-loop pairs yield four ground states in the ideal model.
How it appears in quantum phenomena
Toric code is a canonical quantum error-correcting model of $\mathbb Z_2$ topological order.
Assumptions, caveats and limitations
Finite temperature and local noise can destroy stored information; the 2D toric code is not self-correcting at finite temperature.
Connect the ideas
For context, see the Interacting Topological Phases topic guide and the reading references.