The geometric order of stripes and luttinger liquids

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 antiphase boundaries in the spin system. We demonstrate that the quantity which is ordering is sublattice parity, referring to the geometrie property of a bipartite lattice that it can be subdivided in two sublattices in two different ways. Reinterpreting 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 are fully taken into account, a perfect sublattice parity order is imposed. Owing to novel order-out-of-disorder physics, the sublattice parity order gives rise to fuli stripe order at long wavelengths. 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-T_c superconductivity.