Factorization of density matrices in the critical RSOS models

We study reduced density matrices of the integrable critical RSOS model in a particular topological sector containing the ground state. Similar as in the spin-$1/2$ Heisenberg model it has been observed that correlation functions of this model on short segments can be `factorized': they are completely determined by a single nearest-neighbour two-point function $\omega$ and a set of structure functions. While $\omega$ captures the dependence on the system size and the state of the system the structure functions can be expressed in terms of the possible operators on the segment, in the present case representations of the Temperley-Lieb algebra $\text{TL}_n$, and are independent of the model parameters. We present explicit results for the function $\omega$ in the infinite system ground state of the model and compute multi-point local height probabilities for up to four adjacent sites for the RSOS model and the related three-point correlation functions of non-Abelian $su(2)_k$ anyons.