The density matrix renormalization (DMRG) group method for ladders works much more efficiently with open boundary conditions. One consequence of these boundary conditions is ground-state charge density oscillations that often appear to be nearly constant in magnitude or to decay only slightly away from the boundaries. We analyze these using bosonization techniques, relating their detailed form to the correlation exponent and distinguishing boundary induced generalized Friedel oscillations from true charge density waves. We also discuss a different approach to extracting the correlation exponent from the finite size spectrum which uses exclusively open boundary conditions and can therefore take advantage of data for much larger system sizes. A general discussion of the Friedel oscillation wave vectors is given, and a convenient Fourier transform technique is used to determine it. DMRG results are analyzed on Hubbard and $t\ensuremath{-}J$ chains and 2 leg $t\ensuremath{-}J$ ladders. We present evidence for the existence of a long-ranged charge density wave state in the $t\ensuremath{-}J$ ladder at a filling of
n=0.75 and near $J/t\ensuremath{\approx}0.25.$
We investigate hard-core bosons at half filling on a three-leg ladder under the uniform artificial gauge field. By analyzing current patterns and correlation functions, we uncover a rich quantum phase diagram containing multiple superfluid and insulating phases. In bosonic ladder systems, increasing the gauge flux typically destabilizes the Meissner phase and leads to vortex phases characterized by circulating currents. In the present system, however, we find that charge-density-wave (CDW) phases emerge precisely in such a flux regime despite the presence of only an on-site interaction, where vortex states are naturally expected and are indeed realized in nearby parameter regions. While part of this behavior can be qualitatively understood from a strong-coupling perspective, we also identify an isolated CDW region that cannot be connected to such limits. Furthermore, upon increasing the artificial gauge flux, we observe a reentrant sequence of quantum phase transitions, CDW
→ vortex-superfluid
→ CDW, revealing a strong competition between the vortex phase and the density-wave order.
In the weak-coupling limit, we investigate two-leg ladders with a unit cell containing both Cu and O atoms as a function of doping. For purely repulsive interactions, using bosonization, we find significant differences with the single-orbital case: a completely massless quantum critical regime is obtained for a finite range of carrier concentration. In a broad region of the phase diagram, the ground state consists of a pattern of orbital currents plus a density wave. NMR properties of the Cu and O nuclei are presented for the various phases.