New evidence for 'confined coherence' in weakly coupled Luttinger liquids

On the basis of a calculation of the exact inter-liquid hopping rate and an approximate single-particle Green's function, we present new evidence for the existence of a phase of relevant but incoherent inter-Luttinger-liquid transport. This phase of 'confined coherence' occurs when the Luttinger liquid exponent alpha satisfies alpha(c) < alpha < 1/2. We argue that a, is strictly bounded above by 1/4, and is probably substantially smaller, especially in spin-charge-separated Luttinger liquids. We also discuss connections with the work of others.