Quantum critical scaling behavior of deconfined spinons

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 $\mathrm{SU}\left(N\right)$ 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 $ϵ=4-d$. We also note the scaling relation $\eta =d+2(1-\phi ∕\nu )$ connecting the exponent $\eta$ for the decay to the correlation length exponent $\nu$ and the crossover exponent $\phi$.