where α and β are relative interaction strengths compared to spin interactions along the plaquette edge. The energy spectrum E□ of a single plaquette Hamiltonian is shown in Fig. 2(b), as a function of the parameters α and β. Importantly, there exists a parameter regime 0<2−β<α<2+β with 0<β<1, where the odd parity states are degenerate and have a lower energy than the even parity states. As the precise value of the gap in Fig. 2 is not relevant, as long as it exceeds all other energy scales, is quite robust against small variations in interaction strengths, and the parameters α, β need not be fine-tuned.