Quasi-one-dimensional dynamics and nematic phases in the two-dimensional Emery model

We consider the Emery model of a Cu-O plane of the high-temperature superconductors. We show that in a strong-coupling limit, with strong Coulomb repulsions between electrons on nearest-neighbor O sites, the electron dynamics is strictly one dimensional, and consequently a number of asymptotically exact results can be obtained concerning the electronic structure. In particular, we show that a nematic phase, which spontaneously breaks the point-group symmetry of the square lattice, is stable at low enough temperatures and strong enough coupling.