  We compute a variational approximation to the entanglement entropy for states
of the Gross-Neveu model. Further, we examine the functional dependence of the
entanglement entropy on the coupling and number of colors in the theory. Our
results display non-peturbative behavior. It is shown that the entanglement
entropy is monotonically decreasing and convex with respect to the coupling. We
also show how the behavior of the entanglement entropy under renormalization
group transformations is related to the beta function of the Gross-Neveu model,
and compare these renormalization group results to our previous work on
interacting scalar field theories.
