Néel ordered versus quantum disordered behavior in doped spin-Peierls and Haldane gap systems

I consider a theoretical description of recent experiments on doping the spin-Peierls compound CuGeO3 and the Haldane gap compounds PbNi2V2O8 and Y2BaNiO5. The effective theory is the one of randomly distributed spin-1/2 moments interacting with an exchange decaying exponentially with distance. The model has two phases in the (doping, interchain coupling) plane: (i) a Néel ordered phase at small doping; (ii) a quantum disordered phase at larger doping and small interchain interactions. The spin-Peierls compound CuGeO3 and the Haldane gap nickel oxides PbNi2V2O8 and Y2BaNiO5 fit well into this phase diagram. At small temperature, the Néel phase is found to be reentrant into the quantum disordered region. The Néel transition relevant for CuGeO3 and PbNi2V2O8 can be described in terms of a classical disordered model. A simplified version of this model is introduced, and is solved on a hierarchical lattice structure, which allows to discuss the renormalization group flow of the model. It is found that the system looks non disordered at large scale, which is not against available susceptibility experiments. In the quantum disordered regime relevant for Y2BaNiO5, the two spin model and the cluster RG in the 1D regime show a power law susceptibility, in agreement with recent experiments on Y2BaNiO5. It is found that there is a succession of two distinct quantum disordered phases as the temperature is decreased. The classical disordered model of the doped spin-1chain contains already a physics relevant to the quantum disordered phase.