  In this article we consider physical states in the hypercuboidal truncation
of the EPRL-FK spin foam quantum gravity model. In particular, these states are
defined on graphs which allow considering the entanglement entropy (EE)
associated to the bipartition of space. We compute the EE numerically for some
examples, and find that it depends on the coupling constants within the theory.
We also find that there appears a maximum of the EE within the region of the
coupling constant containing the non-Gaussian fixed point of the RG flow of the
truncated model. We discuss the relation of this behaviour with the restoration
of diffeomorphism symmetry at the fixed point.
