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

Abstract

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 ${D}_{c}\ensuremath{\simeq}0.1J$ using exact diagonalizations and finite-size scaling. This suggests that the kagome compound ${\text{ZnCu}}_{3}{(\text{OH})}_{6}{\text{Cl}}_{3}$ may be in a quantum critical region controlled by this fixed point.