  We consider a bilayer quantum spin model with anisotropic intra-layer
exchange couplings. By varying the anisotropy, the quantum critical phenomena
changes from XY to Heisenberg to Ising universality class, with two, three and
one modes respectively becoming gapless simultaneously. We use series expansion
methods to calculate the second and third Renyi entanglement entropies when the
system is bipartitioned into two parts. Leading area-law terms and subleading
entropies associated with corners are separately calculated. We find clear
evidence that the logarithmic singularity associated with the corners is
universal in each class. Its coefficient along the Ising critical line is in
excellent agreement with those obtained previously for the transverse-field
Ising model. Our results provide strong evidence for the idea that the
universal terms in the entanglement entropy provide an approximate measure of
the low energy degrees of freedom in the system.
