Quantum phases of SU(N) spins on a diamond lattice

We study the SU(N) generalization of the Heisenberg antiferromagnet on the diamond lattice. We use the stochastic series expansion QMC method to compute properties of and hence deduce the ground states of the model as we vary N. We find that the magnetic order present for N=2 is destroyed for all N$>$9. The nature of the non-magnetic state is studied paying particular attention to the nature of valence bond solid ordering and the possibility of a quantum spin liquid. The nature of the phase transition between different phases is investigated.