Chirally stabilized critical state in marginally coupled spin and doped systems

Abstract 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.