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

physical review. b./physical review. b

Average eigenstate entanglement entropy of the XY chain in a transverse  field and its universality for translationally invariant quadratic fermionic  models