  We develop a method to calculate the bipartite entanglement entropy of
quantum models, in the thermodynamic limit, using a Numerical Linked Cluster
Expansion (NLCE) involving only rectangular clusters. It is based on exact
diagonalization of all n x m rectangular clusters at the interface between
entangled subsystems A and B. We use it to obtain the Renyi entanglement
entropy of the two-dimensional transverse field Ising model, for arbitrary real
Renyi index alpha. Extrapolating these results as a function of the order of
the calculation, we obtain universal pieces of the entanglement entropy
associated with lines and corners at the quantum critical point. They show NLCE
to be one of the few methods capable of accurately calculating universal
properties of arbitrary Renyi entropies at higher dimensional critical points.
