Eigenstate entanglement entropy in the integrable spin-$\frac{1}{2}$ XYZ model

We study the average and the standard deviation of the entanglement entropy of highly excited eigenstates of the integrable interacting spin-$\frac{1}{2}$ XYZ chain away from and at special lines with $U(1)$ symmetry and supersymmetry. We universally find that the average eigenstate entanglement entropy exhibits a volume-law coefficient that is smaller than that of quantum-chaotic interacting models. At the supersymmetric point, we resolve the effect that degeneracies have on the computed averages. We further find that the normalized standard deviation of the eigenstate entanglement entropy decays polynomially with increasing system size, which we contrast to the exponential decay in quantum-chaotic interacting models. Our results provide state-of-the art numerical evidence that integrability in spin-$\frac{1}{2}$ chains reduces the average, and increases the standard deviation, of the entanglement entropy of highly excited energy eigenstates when compared to those in quantum-chaotic interacting models.