  We study the Hubbard model with time-reversal invariant flux and spin-orbit
coupling and position-dependent onsite energies on the kagome lattice, using
numerical and analytical methods. In particular, we perform calculations using
real space dynamical mean-field theory (R-DMFT). To study the topological
properties of the system, we use the topological Hamiltonian approach. We
obtain a rich phase diagram: for weak and intermediate interactions, depending
on the model parameters, the system is in the band insulator, topological
insulator, or metallic phase, while for strong interactions the system is in
the Mott insulator phase. We also investigate the magnetic phases that occur in
this system. For this purpose, in addition to R-DMFT, we also use two
analytical methods: perturbation theory for large interactions and onsite
energies, and stochastic mean-field theory.
