We have used a recently proposed quantum Monte Carlo
algorithm  to study spinons (emergent S = 1/2 excitations) in 2D
Resonating-Valence-Bond (RVB) spin liquids and in a J-Q model hosting a Neel –
Valence Bond Solid (VBS) phase transition at zero temperature . We confirm
that spinons are well defined quasi-particles with finite intrinsic size in the
RVB spin liquid. The distance distribution between two spinons shows signatures
However, at the Neel–VBS transition, we found that the
size of a single spinon is significantly greater than the bound-state in VBS,
which indicates that spinons are “soft” and shrink when bound state is formed.
Both spinon size and confinement length diverge as the critical point is
approached. We have also compared spinon statistics in J-Q model with bilayer
Heisenberg model and 1D spin chain. We conclude that the spinon deconfinement
is marginal in the lowest-energy state in the spin-1 sector, due to very weak
attractive spinon interactions. Deconfinement in the vicinity of the critical
point should occur at higher energies.