Deconfined quantum criticality driven by Dirac fermions in SU(2) antiferromagnets

Quantum electrodynamics in 2+1 dimensions is an effective gauge theory for the so called algebraic quantum liquids. A new type of such a liquid, the algebraic charge liquid, has been proposed recently in the context of deconfined quantum critical points [R. K. Kaul {\it et al.}, Nature Physics {\bf 4}, 28 (2008)]. In this context, we show by using the renormalization group in $d=4-\epsilon$ spacetime dimensions, that a deconfined quantum critical point occurs in a SU(2) system provided the number of Dirac fermion species $N_f\geq 4$. The calculations are done in a representation where the Dirac fermions are given by four-component spinors. The critical exponents are calculated for several values of $N_f$. In particular, for $N_f=4$ and $\epsilon=1$ ($d=2+1$) the anomalous dimension of the N\'eel field is given by $\eta_N=1/3$, with a correlation length exponent $\nu=1/2$. These values change considerably for $N_f>4$. For instance, for $N_f=6$ we find $\eta_N\approx 0.75191$ and $\nu\approx 0.66009$. We also investigate the effect of chiral symmetry breaking and analyze the scaling behavior of the chiral holon susceptibility, $G_\chi(x)\equiv<\bar \psi(x)\psi(x)\bar \psi(0)\psi(0)>$.