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We present an ab initio derivation method for effective low-energyHamiltonians of material with strong spin-orbit interactions. The effectiveHamiltonian is described in terms of the Wannier function in the spinor form,and effective interactions are derived with the constrained random phaseapproximation (cRPA) method. Based on this formalism and the developed code, wederive an effective Hamiltonian of a strong spin-orbit interaction materialCa5Ir3O12. This system consists of three edge-shared IrO6 octahedral chainsarranged along the c axis, and the three Ir atoms in the ab plane compose atriangular lattice. For such a complicated structure, we need to set up theWannier spinor function under the local coordinate system. We found that adensity-functional band structure near the Fermi level is formed by local dxyand dyz orbitals. Then, we constructed the ab initio dxy/dyz model. Theestimated nearest neighbor transfer t is close to 0.2 eV, and the cRPA onsite Uand neighboring V electronic interactions are found to be 2.4-2.5 eV and 1 eV,respectively. The resulting characteristic correlation strength defined by(U-V)/t is above 7, and thus this material is classified as a stronglycorrelated electron system. The onsite transfer integral involved in thespin-orbit interaction is 0.2 eV, which is comparable to the onsite exchangeintegrals near 0.2 eV, indicating that the spin-orbit-interaction physics wouldcompete with the Hund physics. Based on these calculated results, we discusspossible rich ground-state low-energy electronic structures of spin, charge andorbitals with competing Hund, spin-orbit and strong correlation physics.

Ab initio Derivation of Low-Energy Hamiltonians for Systems with Strong Spin-Orbit Interaction and Its Application to Ca5Ir3O12