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<Dc the system is in a moment-free phase, and for D>Dc the system develops antiferromagnetic long-range order. The quantum critical point is found to be Dc0.1J using exact diagonalizations and finite-size scaling. This suggests that the kagome compound ZnCu₃(OH)₆Cl₃ may be in a quantum critical region controlled by this fixed point.