Phase diagram of three-leg ladders at strong coupling along the rungs

We construct a phase diagram of the t - J three-leg ladders as a function o f hole doping in the limit where the coupling parameters along the rungs t( perpendicular to) and J(perpendicular to) are much larger than the coupling parameters t(\\) and J(\\) along the legs. At large exchange coupling alon g the rungs J(perpendicular to)/t(perpendicular to) > 3/root 2 there is a t ransition to Luther-Emery liquid at a critical hole concentration n(crit) a pproximate to 1/3. In the opposite case J(perpendicular to)/t(perpendicular to) < 3/root 2 there is a sequence of three Luttinger liquid phases (LLI, LLII, LLIII) as a function of hole density. (C) 2000 Elsevier Science B.V. All rights reserved.