| We study the antiferromagnetic spin-1/2 Heisenberg model on the highly frustrated, three-dimensional, hyper-kagome lattice using a series expansion around an arbitrary dimerized state. We propose a valence bond crystal with a 72 site unit cell as a ground state that supports many, very low lying, excitations in the singlet sector. Low energy spinful excitations (spinons and triplons) are effectively confined to various emergent lower-dimensional structures. If applicable to the recently studied sodium iridate compound, Na4Ir3O8, this scenario has interesting observable implications, such as spatially anisotropic neutron scattering spectra and possibly multiple finite temperature signatures in the magnetic specific heat due to a multi-step breaking of discrete symmetries. Most saliently, here - as for several proposed states for analogous kagome and pyrochlore magnets - one might expect a clearly resolved Ising transition at relatively high temperature. |
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