Statistics of holons in the quantum hard-core dimer gas

The nature of holons, and in particular, their statistics, are studied in the context of a two-dimensional quantum hard-core dimer gas. This model has been shown to embody the low-energy physics of the short-ranged resonating-valence-bond state. We find that, depending on detailed energetic considerations, the holons either bind a half flux quantum of "statistical flux," in which case they are fermions, or they are free, in which case they are bosons. The exchange energy is shown to favor a fermionic hole while the hole kinetic energy (which generally exceeds the exchange energy) favors bosonic holes. Finally, it is shown that even in the bosonic case, flux quantization is in units of $\frac{\mathrm{hc}}{2e}$.