Observing spinon excitations in quantum spin models

We develop a technique to directly study spinons (emergent spin $S=1/2$ particles) in quantum spin models in any number of dimensions [1]. Two characteristic lengths---the size of a spinon wave packet and the size of a bound pair (a triplon)---are defined in terms of wave-function overlaps that can be evaluated by quantum Monte Carlo simulations. We find that these two lengths are well distinguishable in one-dimensional models with valence-bond-solid (VBS) ground states and explicitly dimerized models, yet hardly separable in 2-leg ladder systems. We provide some physics insights for these phenomena. We also study spinons in two-dimensional resonating-valence-bond states and models with N\'eel-VBS transitions.\\[4pt] [1] Y. Tang and A. W. Sandvik, Phys. Rev. Lett. 107, 157201 (2011).