Non-Kramers spin liquids on the pyrochlore lattice

At low temperatures the pyrochlore iridates Pr$_2$Ir$_2$O$_7$ shows the puzzling combination of an anomalous Hall effect in the absence of experimentally observed magnetic order. The breaking of time-reversal symmetry indicated by the anomalous Hall effect, but without the usual accompanying magnetic order, points to an exotic state, possibly a chiral spin liquid. Considering the most general symmetry allowed model for the Pr non-Kramers doublets, we use the slave-fermion approach to analyze possible spin liquids at the mean field level. A variety of spin liquids can be generated using the projective symmetry group, with novel properties due to the nature of the non-Kramers doublet states. Applications to Pr$_2$Ir$_2$O$_7$ will be discussed.