  We studied single and two Su-Shreiffer-Heeger wires on a simple cubic
semiconducting substrate. The wire-wire coupling is either perpendicular or
diagonal hopping respecting the particle-hole and time-reversal symmetries. The
hybridization to the substrate renormalizes the model parameters of the wires
towards the hopping parameter of the substrate without changing the basic
nature of perpendicular or diagonal coupling and it can mediate effective
perpendicular hopping but not diagonal hopping in the absence of direct
wire-wire coupling. This justifies the investigation of multi uniform tight
binding wires with perpendicular or diagonal hopping parameters while
neglecting the substrate. Perpendicularly coupled uniform wires reveal an
anisotropic two dimensional band dispersion. Diagonally coupled uniform wires
reveal strictly one dimensional bands parallel to the wires direction if the
intra-wire hopping parameter is larger than twice the diagonal hopping
parameter despite strong dispersion perpendicular to the wires. Otherwise, they
reveal strictly one dimensional bands parallel and perpendicular to the wires
direction simultaneously. We established the possibility of realizing strictly
one dimensional properties emerging from dispersive two dimensional systems if
time-reversal and particle-hole symmetries are respected. This can facilitate
the investigations of Luttinger liquid in the Au/Ge(001) and Bi/InSb(001)
surface reconstructions.
