### Speaker

### Description

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 correlation functions of this model on

short segments can be `factorized': they are completely determined by

a single nearest-neighbour two-point function $\omega$ capturing the

dependence on the system size and the state of the system and a set of

structure functions. The latter 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.