Ordering from frustration in a strongly correlated one-dimensional system

We study a one-dimensional extended Hubbard model with longer-range Coulomb interactions at quarter-filling in the strong coupling limit. We find two different charge-ordered (CO) ground states as the strength of the longer range interactions is varied. At lower energies, these CO states drive two different spin-ordered ground states. A variety of response functions computed here bear a remarkable resemblance to recent experimental observations for organic TMTSF systems, and so we propose that these systems are proximate to a QCP associated with T=0 charge order. For a ladder system relevant to $Sr_{14}Cu_{24}O_{41}$, we find in-chain CO, rung-dimer, and orbital antiferromagnetic ordered phases with varying interchain couplings and superconductivity with hole-doping. RPA studies of many chains (ladders) coupled reveal a phase diagram with the ordered phase extended to finite temperatures and a phase boundary ending at a quantum critical point (QCP). Critical quantum fluctuations at the QCP are found to enhance the transverse dispersion, leading to a dimensional crossover and a T=0 decofinement transition.