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We apply the quasiparicle self-consistent $GW$ (\qsgw) method to a cubicvirtual-crystal alloy La$_{1-x}$Ba$_x$MnO$_3$ %(LBMO) as a theoreticalrepresentative for colossal magnetoresistive perovskite manganites. The \qsgw\predicts it as a fully-polarized half-metallic ferromagnet for a wide range of$x$ and lattice constant. Calculated density of states and dielectric functionsare consistent with experiments. In contrast, the energies of calculated spinwave are very low in comparison with experiments. This is affected neither byrhombohedral deformation nor the intrinsic deficiency in the \qsgw method. Thuswe ends up with a conjecture that phonons related to the Jahn-Teller distortionshould hybridize with spin waves more strongly than people thought until now.

Re-examination of half-metallic ferromagnetism for doped LaMnO3 in quasiparticle self-consistent $GW$ method