Fig. 2
The mapping to a Toric code on a honeycomb superlattice. a Star dimer pattern selected from spin waves16. The numbers 1–10 label the spin sites, and the shaded 3×1 vectors below each number give the corresponding Cartesian components. The star pattern is one of the Cartesian states of Fig. 1b, which map to dimer (yellow) coverings on the lattice. The η’s describe the orientation of the two spins per dimer. They sit at the middle of the bonds of a honeycomb superlattice (dashed). b The resulting Toric code description of Eq. (10) on the honeycomb superlattice. The three- and six-body operators A v and B p of Eq. (10) are defined on vertices v and plaquettes p of the superlattice. These connect, respectively, three sites (v1–v3) and six sites (p1–p6) of the superlattice. For the torus geometry, CX1 and CX2 (similarly for CZ1 and CZ2) are non-contractible loops that wrap the system in different directions
