Quasi-one-dimensional organic conductors: dimensional crossover and some puzzles

We review some properties of quasi-one-dimensional organic conductors, such as the Bechgaard salts, with an emphasis on aspects related to the crossovers between a Mott insulating state to a metallic state, and crossovers between different metallic behaviors. We discuss why a theoretical description of these issues is a particularly challenging problem, and describe a recent non-perturbative approach designed to deal with systems of coupled chains. This method, dubbed "chain-DMFT", is a generalization of dynamical mean field theory that treats both, one-dimensional and higher dimensional physics, in a unified manner. We present numerical results for a system of coupled Hubbard chains. Chain-DMFT indeed captures the metal-insulator transition and the dimensional crossover from a high temperature Luttinger liquid to a low temperature Fermi liquid phase, and allows to access the properties of these phases. Based on these results perspectives for a theoretical understanding of the physics of the Bechgaard salts are discussed.