Weakly coupled one-dimensional Mott insulators

We consider a model of one-dimensional Mott insulators coupled by a weak interchain tunnelling $t_\perp$. We first determine the single-particle Green's function of a single chain by exact field-theoretical methods and then take the tunnelling into account by means of a Random Phase Approximation (RPA). In order to embed this approximation into a well-defined expansion with a small parameter, the Fourier transform $T_\perp(k)$ of the interchain coupling is assumed to have a small support in momentum space such that every integration over transverse wave vector yields a small factor $\kappa_0^2 \ll 1$. When \tp(0) exceeds a critical value, a small Fermi surface develops in the form of electron and hole pockets. We demonstrate that Luttinger's theorem holds both in the insulating and in the metallic phases. We find that the quasi-particle residue $Z$ increases very fast through the transition and quickly reaches a value of about $0.4-0.6$. The metallic state close to the transition retains many features of the one-dimensional system in the form of strong incoherent continua.