We perform a renormalization group analysis of some important effective field theoretic models for deconfined spinons. We show that deconfined spinons are critical for an isotropic SU(N) Heisenberg antiferromagnet, if $N$ is large enough. We argue that nonperturbatively this result should persist down to N=2 and provide further evidence for the so called deconfined quantum criticality scenario. Deconfined spinons are also shown to be critical for the case describing a transition between quantum spin nematic and dimerized phases. On the other hand, the deconfined quantum criticality scenario is shown to fail for a class of easy-plane models. For the cases where deconfined quantum criticality occurs, we calculate the critical exponent $eta$ for the decay of the two-spin correlation function to first-order in $epsilon=4-d$. We also note the scaling relation $eta=d+2(1-phi/ u)$ connecting the exponent $eta$ for the decay to the correlation length exponent $ u$ and the crossover exponent $phi$.
Download