Fig. 1: Lattice geometry.

Illustration of an XC6 cylinder on a honeycomb lattice. ηγ is +1 (−1) for horizontal (zigzag) bonds. The insets are (left) the unit cell for the zigzag/stripy order with a1 = 3 and \({a}_{2}=\sqrt{3}\), (middle) the hexagonal plaquette operator \({\hat{W}}_{{\rm{p}}}\) with its six sites enumerated, and (right) the X (red), Y (green), and Z (blue) bonds.