Quantum phase transition induced by Dzyaloshinskii-Moriya interactions in the kagome antiferromagnet

We argue that the $S=1/2$ kagome antiferromagnet undergoes a quantum phase transition when the Dzyaloshinskii-Moriya coupling is increased. For $D<D_c$ the system is in a moment-free phase, and for $D>D_c$ the system develops antiferromagnetic long-range order. The quantum critical point is found to be $D_c\simeq 0.1J$ using exact diagonalizations and finite-size scaling. This suggests that the kagome compound ${\text{ZnCu}}_3{\left(\text{OH}\right)}_6{\text{Cl}}_3$ may be in a quantum critical region controlled by this fixed point.