  It is argued that the electron stripes as found in correlated oxides have to
do with an unrecognized form of order. The manifestation of this order is the
robust property that the charge stripes are at the same time anti-phase
boundaries in the spin system. We demonstrate that the quantity which is
ordering is sublattice parity, referring to the geometric property of a
bipartite lattice that it can be subdivided in two sublattices in two different
ways. Re-interpreting standard results of one dimensional physics, we
demonstrate that the same order is responsible for the phenomenon of
spin-charge separation in strongly interacting one dimensional electron
systems. In fact, the stripe phases can be seen from this perspective as the
precise generalization of the Luttinger liquid to higher dimensions. Most of
this paper is devoted to a detailed exposition of the mean-field theory of
sublattice parity order in 2+1 dimensions. Although the quantum-dynamics of the
spin- and charge degrees of freedom is fully taken into account, a perfect
sublattice parity order is imposed. Due to novel order-out-of-disorder physics,
the sublattice parity order gives rise to full stripe order at long wavelength.
This adds further credibility to the notion that stripes find their origin in
the microscopic quantum fluctuations and it suggests a novel viewpoint on the
relationship between stripes and high Tc superconductivity.
