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

A phase diagram of the t-J three-leg ladder as a function of hole doping is derived in the limit where the coupling parameters along the rungs, t(perp endicular to) and J(perpendicular to), are taken to be much larger than tho se along the legs, t(parallel to) and J(parallel to). At large exchange cou pling along the rungs, J(perpendicular to)/t(perpendicular to) > 3/root 2, there is a transition from a low-doping Luttinger liquid phase into a Luthe r-Emery liquid at a critical hole concentration n(crit) approximate to 1/3. in the opposite case, J(perpendicular to)/t(perpendicular to) > 3/ root 2, there as a sequence of three Luttinger liquid phases (LLI, LLII and LLIII) as a function of hole doping. (C) 1999 Elsevier Science B.V. All rights re served.