  We study the fully gapped chiral Mott insulator (CMI) of frustrated
Bose-Hubbard models on ladders and two-dimensional lattices by perturbative
strong-coupling analysis and density matrix renormalization group (DMRG). First
we show the existence of a low-lying exciton state on all geometries carrying
the correct quantum numbers responsible for the condensation of excitons and
formation of the CMI in the intermediate interaction regime. Then we perform
systematic DMRG simulations on several two-leg ladder systems with $\pi$-flux
and carefully characterize the two quantum phase transitions. We discuss the
possibility to extend the generally very small CMI window by including
repulsive nearest-neighbour interactions or changing density and coupling
ratios.
