Entanglement in the open XX chain: Rényi oscillations, hard-edge crossover, and symmetry resolution

We derive closed-form asymptotic formulas for the Rényi entanglement entropies of the open XX spin-1/2 chain by mapping the underlying determinant of the boundary correlation matrix (which has Toeplitz-plus-Hankel structure) to a Hankel determinant with a positive weight whose large-size asymptotics follow from known Riemann--Hilbert results. An explicit evaluation of the Szegő function yields the leading 2k_F oscillatory amplitude and phase. A single variable s = 2ell sin\(k_F/2\) organizes the hard-edge crossover as the Fermi momentum approaches the band edge: the oscillation envelope obeys s^pm1/α power laws and ln s is the natural leading logarithm for a clean data collapse. For detached blocks the oscillatory amplitude is numerically consistent with a factorization through the conformal cross-ratio. The same framework recovers the open-boundary-condition (OBC) equipartition offset -tfrac{1}{2}loglogell for symmetry-resolved entropies, together with the known halving of the Gaussian width relative to the periodic chain.