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 $\tp$ and introduce a systematic diagrammatic expansion in powers of $\tp$. An analysis of the scaling of the diagrams at each order allows us to determine the power-law behavior versus $\tp$ 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 $\tp$ for the self-energy.