Confinement and deconfinement of spinons in two dimensions

Ying Tang and Anders W. Sandvik

Accepted Tuesday Apr 30, 2013

We use Monte Carlo methods to study spinons in two-dimensional quantum spin systems, characterizing their intrinsic size l and confinement length L. We confirm that spinons are deconfined, L and l finite, in a resonating valence-bond spin-liquid state. In a valence-bond solid (VBS), we find finite l and L, with l of a single spinon significantly larger than the bound-state-the spinon is soft and shrinks as the bound state is formed. Both l and L diverge upon approaching the critical point separating VBS and Néel ground states. We conclude that the spinon deconfinement is marginal in the lowest-energy state in the spin-1 sector, due to weak attractive spinon interactions. Deconfinement in the vicinity of the critical point should occur at higher energies.