Gapless spin liquids on the three dimensional hyper-kagome lattice of   Na$_4$Ir$_3$O$_8$
  Recent experiments indicate that Na$_4$Ir$_3$O$_8$, a material in which s=1/2 iridium local moments form a three dimensional network of corner-sharing triangles, may have a quantum spin liquid ground state with gapless spin excitations. Using a combination of exact diagonalization, symmetry analysis of fermionic mean field ground states and Gutzwiller projected variational wavefunction studies, we propose a quantum spin liquid with spinon Fermi surfaces as a favorable candidate for the ground state of the Heisenberg model on the hyper-kagome lattice of Na$_4$Ir$_3$O$_8$. We present a renormalized mean field theory of the specific heat of this spin liquid and also discuss possible low temperature instabilities of the spinon Fermi surfaces. 
Michael Lawler (Toronto), Arun Paramekanti (Toronto), Yong Baek Kim   (Toronto), Leon Balents (UCSB/KITP)