## Confinement and Deconfinement of Spinons in Two Dimensions    [PDF]

Ying Tang, Anders W. Sandvik
Spinons are emergent fractional (spin-1/2) excitations of quantum magnets. While they are well established and understood in one dimension, characterizing them in two-dimensions, in theoretical models and real materials, has been challenging. Here we use Monte Carlo methods to study spinons in a resonating valence-bond (RVB) spin-liquid, as well as in a model which can be tuned from an antiferromagnet to a valence-bond solid (VBS); a crystal of singlets. We use a generalized valence-bond basis to compute the intrinsic size $\lambda$ of an individual spinon and the size $\Lambda$ of a bound state. We confirm that spinons are deconfined, $\Lambda \to \infty$ and $\lambda$ finite, in the RVB. In the VBS $\lambda > \Lambda$, i.e., the spinon is soft and shrinks as the bound state is formed. Both $\lambda$ and $\Lambda$ diverge at the VBS-antiferromagnetic critical point. We conclude that the spinon deconfinement is marginal in the lowest-energy state in the spin-1 sector, due to weak attractive spinon-spinon interactions. Deconfinement should occur at higher energies.
View original: http://arxiv.org/abs/1301.3207