Numerical studies of multi-orbital Hubbard models

This thesis examines the emergence of exotic phases in multi-orbital Hubbard models due to competition between Coulomb interaction, spin-orbit coupling and kinetic energy. Exact diagonalization and numerically accurate density matrix renormalization group methods are used to study small clusters and one dimensional chains. Two dimensional lattices are solved using unrestricted real-space Hartree-Fock approximation. Novel excitonic insulators, due to condensation of spin-orbit excitons, are found in the spin-orbit coupling vs Coulomb interation phase diagrams of (t_2g)ⁿ systems for n = 4 and 3.5. Moreover, the presence of a BCS-BEC crossover in the (t_2g)4 excitonic insulator is predicted. Finally, interesting features in the dynamical spin structure factor calculated using the three-orbital Hubbard model relevant for BaFe₂Se₃ are discussed in detail.