Search for simplex solid and spin liquid phases in highly frustrated S=1 antiferromagnets

Quantum spin liquids are enigmatic phases of matter characterized by the absence of symmetry breaking and conventional quasiparticles. The search for their realisation in actual magnetic materials has targeted, but is not limited to, materials involving the geometrically frustrated triangular, kagome and pyrochlore geometries with low spins. Indeed, while there have been significant efforts to synthesize quantum spin liquid materials in spin-1/2 systems in two dimensions, fewer efforts have been devoted to three dimensions and higher spins. In this talk, we show that both these criteria may be too restrictive. We thus expand our search to spin-1 frustrated antiferromagnets which are abundant in nature but where few theories or results exist to understand their general properties and behavior. Motivated by recent realizations of S=1 kagome and pyrochlore geometries, we address the question of their quantum many-body ground state. For kagome, a spin liquid state known as the Hexagonal Singlet State, motivated by the Affleck Kennedy Lieb Tasaki state in one dimension, is found to be competitive in energy. However, for the pure Heisenberg model it loses out to a symmetry broken trimerized (simplex solid) ground state, a conclusion we derive from density matrix renormalization group calculations. We show that this finding is relevant to the recently synthesized S=1 kagome material Na₂Ti₃Cl₈ which shows a large trimerized distortion in its low temperature phase. For the S=1 pyrochlore case, our search bears fruit - we find a nearly idealized Heisenberg model in NaCaNi₂F₇. Our results show strong evidence for a quantum spin liquid phase based on both its static and dynamical properties.