for reducing computational costs. With the use of the effective Hamiltonian of Wannier-like functions in LDA+DMFT, only a few adopted bands are discussed with fixing the hybridization mixing and could not describe a possible change of hybridization due to local Coulomb interaction.

To carry out calculations in realistic materials with multiple-orbitals, approximate calculation schemes of IPT or NCA could be more suitable because of its efficient CPU-time, though IPT is not applicable to cases of large Coulomb interactions and NCA cannot yield the Fermi liquid behavior at low energies and in low temperature limit. [@re:NCA-error]

The IPT method was developed by Kajueter and Kotliar for non-degenerate orbital and the results show good agreements with the ED results. [@re:Kaj-IPT] However, it was reported that the quasiparticle peak in the IPT results tends to be sharper [@re:Rev-DMFT] and that the IPT results in La$_{1-x}$Sr$_x$TiO$_3$ does not reprduce quasiparticle peak at 1000K. [@re:Nekrasov-LaSrTiO3]

We generalized IPT for multi-orbital bands and applied this method to doubly degenerated ${\mbox{e}_{g}}$ bands and triply degenerated ${\mbox{t}_{2g}}$ bands on simple cubic and body-centered cubic lattices. [@re:Fuji; @re:miura] We also verified that this DMFT with IPT scheme is fairly applicable to arbitrary electron occupation cases with different Coulomb interaction 