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 et al., Nat. Phys. 4, 28 (2008)]. In this context, by using the renormalization group in $d=4-\epsilon$ space-time dimensions, we show that a deconfined quantum critical point occurs in a SU(2) system provided the number of Dirac fermion species $N_f\ge 4$. 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 $\epsilon =1$ $\left(d=2+1\right)$, the anomalous dimension of the Néel field is given by ${\eta }_N=1/3$, with a correlation length exponent $\nu =1/2$. These values considerably change 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, $G_{\chi }\left(x\right)\equiv ⟨\overline{\psi }\left(x\right)\psi \left(x\right)\overline{\psi }\left(0\right)\psi \left(0\right)⟩$.

Figure 1

Schematic flow diagram associated with the $\beta$ functions (22, 23) for $N_b=2$ and $N_f\ge 4$. In the figure, $P_{\pm }=\left(g_{\pm },f_{\ast }\right)$. Note that only $P_{+}$ is infrared stable, thus corresponding to a quantum critical point. For a vanishing gauge coupling, we have a second-order phase transition governed by a O(4) Wilson–Fisher fixed point. This fixed point is unstable for $f\ne 0$.

Figure 2

One-loop Feynman diagrams representing the insertion of the operator ${\left|z_1\right|}^2$ (dashed line) in the correlation function $⟨z_1\left(x\right)z_1^{\ast }\left(0\right)⟩$. Here, the lines labeled 1 or 2 are associated with the fields $z_1$ and $z_2$, respectively. The wavy line represents the gauge field propagator.

Figure 3

For the insertion of the operator ${\left|z_2\right|}^2$ (dashed line) in the correlation function $⟨z_1\left(x\right)z_1^{\ast }\left(0\right)⟩$, only one diagram contributes.