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Topological insulators in the presence of strong Coulomb interactionconstitute novel phases of matter. Transitions between these phases can bedriven by single-particle or many-body effects. On the basis of {\it ab-initio}calculations, we identify a concrete material, {\it i.e.} Ca$_{2}$PtO$_{4}$,that turns out to be a hole-doped weak topological insulator. Interestingly,the Pt-$d$ orbitals in this material are relevant for the band inversion thatgives rise to the topological phase. Therefore, Coulomb interaction should beof importance in Ca$_{2}$PtO$_{4}$. To study the influence of interactions onthe weak topological insulating phase, we look at a toy model corresponding toa layer-stacked 3D version of the Bernevig-Hughes-Zhang model with localinteractions. For small to intermediate interaction strength, we discover novelinteraction-driven topological phase transitions between the weak topologicalinsulator and two Dirac semimetal phases. The latter correspond to gaplesstopological phases. For strong interactions, the system eventually becomes aMott insulator.

Interacting weak topological insulators and their transition to Dirac semimetal phases