Using the properties of the local Boltzmann weights of integrable
interaction-round-a-face (IRF or face) models we express local operators
in terms of generalized transfer matrices. This allows for the
derivation of discrete functional equations for the reduced density
matrices in inhomogeneous generalizations of these models. We apply
these equations to study the density matrices for IRF models of various
solid-on-solid type and quantum chains of non-Abelian
\mathbold{su(2)_3}𝐬𝐮(2)3
or Fibonacci anyons. Similar as in the six vertex model we find that
reduced density matrices for a sequence of consecutive sites can be
‘factorized’, i.e. expressed in terms of nearest-neighbour correlators
with coefficients which are independent of the model parameters.
Explicit expressions are provided for correlation functions on up to
three neighbouring sites.