Matrix product operator representations for the local conserved quantities of the spin-$1/2$ XYZ chain
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909989932630016 |
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| author | Fukai, Kohei Yamada, Kyoichi |
| author_facet | Fukai, Kohei Yamada, Kyoichi |
| contents | We present explicit matrix product operator (MPO) representations for the local conserved quantities of the spin-$1/2$ XYZ chain. Through these MPO representations, we simplify the coefficients appearing in the local conserved quantities originally derived by one of the authors, and reveal their combinatorial meaning: the coefficients prove to be a polynomial generalization of the Catalan numbers, defined via weighted monotonic lattice paths. Furthermore, we obtain a new simple $3 \times 3$ Lax operator for the XYZ chain that, unlike Baxter's R-matrix, does not involve elliptic functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09245 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Matrix product operator representations for the local conserved quantities of the spin-$1/2$ XYZ chain Fukai, Kohei Yamada, Kyoichi Exactly Solvable and Integrable Systems Statistical Mechanics Mathematical Physics We present explicit matrix product operator (MPO) representations for the local conserved quantities of the spin-$1/2$ XYZ chain. Through these MPO representations, we simplify the coefficients appearing in the local conserved quantities originally derived by one of the authors, and reveal their combinatorial meaning: the coefficients prove to be a polynomial generalization of the Catalan numbers, defined via weighted monotonic lattice paths. Furthermore, we obtain a new simple $3 \times 3$ Lax operator for the XYZ chain that, unlike Baxter's R-matrix, does not involve elliptic functions. |
| title | Matrix product operator representations for the local conserved quantities of the spin-$1/2$ XYZ chain |
| topic | Exactly Solvable and Integrable Systems Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2601.09245 |