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 ${D}_{c}\ensuremath{\simeq}0.1J$ 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.
We investigate the zero-temperature phase diagram of the nearest-neighbor kagome antiferromagnet in the presence of Dzyaloshinksii-Moriya interaction. We develop a theory for the transition between
Z2 spin liquids with bosonic spinons and a phase with antiferromagnetic long-range order. Connections to recent numerical studies and experiments are discussed.
Motivated by experimental results for the thermodynamic properties of the Rb 2 Cu 3 SnF 12 material and the discovery of its valence-bond solid ground state, we utilize the numerical linked-cluster expansions (NLCEs) and devise an expansion tailored to solve the Heisenberg model on a pinwheel-distorted kagome lattice. Using the exchange interactions that are relevant to Rb 2 Cu 3 SnF 12 , we calculate its uniform spin susceptibility and find a very good agreement with experiment. Next, we focus on the ground state of a simplified model of the distorted kagome lattice and take advantage of a zero-temperature Lanczos-based NLCE to study the approach to the ground state of the uniform kagome lattice Heisenberg model using a tuning parameter. Together with results from exact diagonalization of finite clusters, we find evidence that a phase transition occurs before the uniform limit is reached.