Simplex solid and spin liquid phases in two dimensional frustrated kagome antiferromagnets

Strongly correlated systems provide a fertile ground for discovering exotic states of matter, for example, those with topologically non-trivial properties. Among these are frustrated magnets, which are now being studied with advanced numerical many-body techniques. I present two of our works in this area, both focusing on the kagome geometry which has near-ideal realizations in several materials, often with an onsite spin-moment that is greater than 1/2. First, I present a study of the spin-1 Heisenberg antiferromagnet, where contrary to several previous theoretical proposals, our calculations indicate that the ground state is a valence bond (simplex) solid with a spin gap that is consistent with experimental findings. In the second part, I consider the spin-1/2 XXZ model in a magnetic field, equivalent to a hard-core bosonic problem with density-density interactions at finite filling fraction. Motivated by previous field theoretical studies, I focus my attention to understanding the XY limit for the 2/3 magnetization plateau (i.e. 1/6 filling of bosons). We perform exact or accurate numerical computations to search for the predicted chiral spin liquid and based on energetics and the determination of minimally entangled states and the associated modular matrices, provide evidence for this phase.