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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2604.05356 |
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| _version_ | 1866915919769370624 |
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| author | Tierz, Miguel |
| author_facet | Tierz, Miguel |
| contents | 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 $s = 2\ell \sin(k_F/2)$ 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 $-\tfrac{1}{2}\log\log\ell$ for symmetry-resolved entropies, together with the known halving of the Gaussian width relative to the periodic chain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05356 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Entanglement in the open XX chain: Rényi oscillations, hard-edge crossover, and symmetry resolution Tierz, Miguel Statistical Mechanics Mathematical Physics Quantum Physics 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 $s = 2\ell \sin(k_F/2)$ 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 $-\tfrac{1}{2}\log\log\ell$ for symmetry-resolved entropies, together with the known halving of the Gaussian width relative to the periodic chain. |
| title | Entanglement in the open XX chain: Rényi oscillations, hard-edge crossover, and symmetry resolution |
| topic | Statistical Mechanics Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2604.05356 |