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We study the antiferromagnetic spin-1/2 Heisenberg model on the highlyfrustrated, three-dimensional, hyperkagome lattice of Na_4Ir_3O_8 using aseries expansion method. We propose a valence bond crystal with a 72 site unitcell as a ground state that supports many, very low lying, singlet excitations.Low energy spinons and triplons are confined to emergent lower-dimensionalmotifs. Here, and for analogous kagome and pyrochlore states, we suggest finitetemperature signatures, including an Ising transition, in the magnetic specificheat due to a multistep breaking of discrete symmetries.

Symmetry Breaking on the Three-Dimensional Hyperkagome Lattice of Na_4Ir_3O_8