  We recently showed [Phys. Rev. Lett. 121, 220602 (2018)] that the average
bipartite entanglement entropy of all energy eigenstates of the quantum Ising
chain exhibits a universal (for translationally invariant quadratic fermionic
models) leading term that scales linearly with the subsystem's volume, while in
the thermodynamic limit the first subleading correction does not vanish at the
critical field (it only depends on the ratio $f$ between the volume of the
subsystem and volume of the system) and vanishes otherwise. Here we show,
analytically for bounds and numerically for averages, that the same remains
true for the spin-1/2 XY chain in a transverse magnetic field. We then tighten
the bounds for the coefficient of the universal volume-law term, which is a
concave function of $f$. We develop a systematic approach to compute upper and
lower bounds, and provide explicit analytic expressions for up to the fourth
order bounds.
