Spin Ladders : From 1 to 2 dimensions

Abstract
We first review the general properties of the spin ladder compounds, a new class of low dimensional strongly correlated systems of fermions which exhibit specific original properties. Of particular interest is the versatility of these systems, in some cases reminiscent of quasi-one dimensional conductors, and in other cases reminiscent of quasi-two dimensional high-T_c superconductors, depending on the ladder structure (number of legs), Umklapp scattering, doping of charge carriers, external parameters such as temperature, pressure and magnetic field. The understanding of the dimensional crossover, from one dimension to two dimensions, when these parameters are varied is, therefore, particularly important. A related question is the interplay between the spin gap in the magnetic excitation spectrum and the superconducting temperature under pressure, observed in these compounds, in obvious relationship with high-T_c superconductors physics. To get more insights into the pressure induced superconducting transition, we have focused our interest on doped coupled ladder systems. We have studied the effect of Umklapp process on two-leg Hubbard ladders with half-filled bands which strongly reduces the interladder hopping and promotes SDW correlations at the expense of superconducting ones. To provide information on the confinement-deconfinement phenomenon induced by the hopping process under pressure, we have investigated the orbital effect of a magnetic field on a system of weakly coupled Hubbard ladders, which induces a reduction in the effective dimensionality of the system, by confining the carriers motion within the ladders. We conclude by suggesting promising studies in the context of ladder materials.