  A recent study revealed the dynamics of the charge sector of a
one-dimensional quarter-filled electronic system with extended Hubbard
interactions to be that of an effective pseudospin transverse-field Ising model
(TFIM) in the strong coupling limit. With the twin motivations of studying the
co-existing charge and spin order found in strongly correlated chain systems
and the effects of inter-chain couplings, we investigate the phase diagram of
coupled effective (TFIM) systems. A bosonisation and RG analysis for a two-leg
TFIM ladder yields a rich phase diagram showing Wigner/Peierls charge order and
Neel/dimer spin order. In a broad parameter regime, the orbital
antiferromagnetic phase is found to be stable. An intermediate gapless phase of
finite width is found to lie in between two charge-ordered gapped phases.
Kosterlitz-Thouless transitions are found to lead from the gapless phase to
either of the charge-ordered phases. A detailed analysis is also carried out
for the dimensional crossover physics when many such pseudospin systems are
coupled to one another. Importantly, the analysis reveals the key role of
critical quantum fluctuations in driving the strong dispersion in the
transverse directions, as well as a T=0 deconfinement transition. Our work is
potentially relevant for a unified description of a class of strongly
correlated, quarter-filled chain and ladder systems.
