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

Abstract

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.

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• Normal weak eigenstate thermalization
• Non-abelian symmetry-resolved entanglement entropy
• Weak ergodicity breaking with isolated integrable sectors
• Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians
• Onset of Quantum Chaos and Ergodicity in Spin Systems with Highly Degenerate Hilbert Spaces
• Localization transitions in quadratic systems without quantum chaos