Coordinate-energy transformation and the one-point function for the Heisenberg-Ising XXZ spin-1/2 chain on the ring
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| Format: | Preprint |
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2025
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| _version_ | 1866908410594721792 |
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| author | Corwin, Eric I. Elsaesser, Nikolaus Saenz, Axel |
| author_facet | Corwin, Eric I. Elsaesser, Nikolaus Saenz, Axel |
| contents | We provide a basis transformation that inverts the coordinate Bethe Ansatz. It is widely believed that the Bethe Ansatz is complete, based on numerical evidence and combinatorial arguments. We present a constructive and comprehensive approach to show that the Bethe Ansatz is complete. The transformation formula is verified numerically with excellent accuracy for non-zero anisotropy parameters and rings of odd length. Additionally, assuming the Bethe Ansatz is complete, we derive a novel exact formula for the one-point function systems through special identities for the Izergin-Korepin determinant. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_14171 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coordinate-energy transformation and the one-point function for the Heisenberg-Ising XXZ spin-1/2 chain on the ring Corwin, Eric I. Elsaesser, Nikolaus Saenz, Axel Mathematical Physics Probability 82B23 (Primary) 82B20, 60K35 (Secondary) We provide a basis transformation that inverts the coordinate Bethe Ansatz. It is widely believed that the Bethe Ansatz is complete, based on numerical evidence and combinatorial arguments. We present a constructive and comprehensive approach to show that the Bethe Ansatz is complete. The transformation formula is verified numerically with excellent accuracy for non-zero anisotropy parameters and rings of odd length. Additionally, assuming the Bethe Ansatz is complete, we derive a novel exact formula for the one-point function systems through special identities for the Izergin-Korepin determinant. |
| title | Coordinate-energy transformation and the one-point function for the Heisenberg-Ising XXZ spin-1/2 chain on the ring |
| topic | Mathematical Physics Probability 82B23 (Primary) 82B20, 60K35 (Secondary) |
| url | https://arxiv.org/abs/2506.14171 |