Interchain coherence of coupled Luttinger liquids at all orders in perturbation theory

We analyze the problem of Luttinger liquids coupled via a single-particle hopping parameter t(perpendicular to) and introduce a systematic diagrammatic expansion in powers of t(perpendicular to). An analysis of the scaling of the diagrams at each order allows us to determine the power-law behavior versus t(perpendicular to) of the interchain hopping and of the Fermi surface warp. In particular, for strong interactions, we find that the exponents are dominated by higher-order diagrams producing an enhanced coherence and a failure of linear-response theory. Our results are valid at any finite order in t(perpendicular to) for the self-energy.