  We develop the multi-scale ab-initio scheme for correlated electrons (MACE)
for transitionmetal-oxide heterostructures, and determine the parameters of the
low-energy effective model. By separating Ti t2g bands near the Fermi level
from the global Kohn-Sham (KS) bands of LaAlO3/SrTiO3 which are highly
entangled with each other, we are able to calculate the parameters of the
low-energy effective model of the interface with the help of constrained random
phase approximation (cRPA). The on-site energies of the Ti t2g orbitals in the
1stlayer is about 650 meV lower than those in the 2nd-layer. In the 1st-layer,
the transfer integral of the Ti t2g orbital is nearly the same as that of the
bulk SrTiO3, while the effective screened Coulomb interaction becomes about 10
percent larger than that of the bulk SrTiO3. The differences of the parameters
from the bulk SrTiO3 reduce rapidly with increasing distance from the
interface. Our present versatile method makes it possible to derive effective
ab-initio low-energy models and allows studying interfaces of strongly
correlated electron systems from first principles.
