Exotic Cooperative Quantum Optics of Moire Exciton Superlattices

Z2 lattice gauge theory is the paradigmatic gauge theory for topological order, but on non-trivial topologies Wegner duality fails to match its sectors. We extend the duality to arbitrary topology, mapping each sector to a sector of a new sectorial Ising (SI) model. Topology is encoded in non-local domain-wall patterns; gauge constraints vanish. Simulating an L*L torus sector now needs only L*L qubits with two-body couplings, halving the usual 2L*L qubit, four-body cost, enabling near-term experimental study of Z2 spin liquids and topological transitions.