Coulomb correlations, broken symmetries and dimensionality effects

Within single particle theories occurrence of spatial broken symmetries depend only on nesting. This picture is shown to change dramatically for nonzero Coulomb interactions, where dimensionality plays a much stronger role. We examine the Peierls-Hubbard model in two dimension, and show that while the simple Peierls instability can occur in one, two or three dimension for perfect nesting, the Hubbard interaction destroys this instability for dimensionality greater than one. The spin-Peierls transition is a unique feature of one dimension. The above is also related to the occurrence of antiferromagnetism in two dimension. Recent observation of the vanishing of the spin-Peierls phase and the appearance of an antiferromagnetic phase in TMTTF-salts under pressure can be explained within the present theory.