Depiction of triplon excitations in the cVBS phase. Panel (a) shows an example of a combination of moves induced by J-terms, in analogy with Fig. 12(d) in the sVBS phase. Panels (b) and (c) show how local fluctuations can alter the configuration shown in (a) without changing the position of the spinons. The original position of the spinons and the valence bond patterns are shown with light colors in (a)–(c). In (d) the π/2-domain walls are indicated with gray curves.