We investigate the formation of stripes in $7r\ifmmode\times\else\texttimes\fi{}6$ Hubbard ladders with
4r holes doped away from half filling using the density-matrix renormalization group (DMRG) method. A parallelized code allows us to keep enough density-matrix eigenstates (up to
m=8000) and to study sufficiently large systems (with up to
7r=21 rungs) to extrapolate the stripe amplitude to the limits of vanishing DMRG truncation error and infinitely long ladders. Our work gives strong evidence that stripes exist in the ground state for strong coupling
(U=12t) but that the structures found in the hole density at weaker coupling
(U=3t) are an artifact of the DMRG approach.
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 several 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 $\ensuremath{\pi}$ 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-neighbor interactions or changing density and coupling ratios.