Chirally stabilized critical state in marginally coupled spin and doped systems

We study a class of one-dimensional models consisting of a frustrated (N + 1)-leg spin ladder, its asymmetric doped version as a special example of a Luttinger Liquid in an active environment, and the N-channel Kondo-Heisenberg model away from half-filling. It is shown that these models exhibit a critical phase with generally a non-integer central charge and belong to the class of chirally stabilized spin liquids recently introduced by Andrei, Douglas, and Jerez [Phys. Rev. B 58 (1998) 7619], By allowing anisotropic interactions in spin space, an exact solution in the N = 2 case is found at a Toulouse point which captures all universal properties of the models. At the critical point, the massless degrees of freedom are described in terms of an effective S = 1/2 Heisenberg spin chain and two critical Ising models. The Toulouse limit solution enables us to discuss the spectral properties, the computation of the spin-spin correlation functions as well as the estimation of the NMR relaxation rate of the frustrated three-leg ladder. Finally, it is shown that the critical point becomes unstable upon switching on some weak backscattering perturbations in the frustrated three-leg ladder. (C) 2000 Elsevier Science B.V. All rights reserved.