A symmetry formula for correlation functions in the superintegrable chiral Potts spin chain
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915898265174016 |
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| author | Zhu, Haoran |
| author_facet | Zhu, Haoran |
| contents | We prove an exact finite-volume symmetry formula for two-point functions in the periodic $N$-state superintegrable chiral Potts spin chain. We show that, for every chain length $L$ and every simultaneous eigenvector of the Hamiltonian and the one-site translation operator, the correlations satisfy $\langle Z_0^r Z_R^{\dagger r}\rangle^*=\langle Z_0^r Z_{L-R}^{\dagger r}\rangle$ for $1\leqslant r\leqslant N-1$. Hence, whenever $L$ is even, the midpoint correlation $\langle Z_0^r Z_{L/2}^{\dagger r}\rangle$ is real. Then we generalise the three-state chain case to arbitrary $N$ and to every translation eigensector. This resolves a conjecture of Fabricius and McCoy. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_27930 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A symmetry formula for correlation functions in the superintegrable chiral Potts spin chain Zhu, Haoran Mathematical Physics Statistical Mechanics We prove an exact finite-volume symmetry formula for two-point functions in the periodic $N$-state superintegrable chiral Potts spin chain. We show that, for every chain length $L$ and every simultaneous eigenvector of the Hamiltonian and the one-site translation operator, the correlations satisfy $\langle Z_0^r Z_R^{\dagger r}\rangle^*=\langle Z_0^r Z_{L-R}^{\dagger r}\rangle$ for $1\leqslant r\leqslant N-1$. Hence, whenever $L$ is even, the midpoint correlation $\langle Z_0^r Z_{L/2}^{\dagger r}\rangle$ is real. Then we generalise the three-state chain case to arbitrary $N$ and to every translation eigensector. This resolves a conjecture of Fabricius and McCoy. |
| title | A symmetry formula for correlation functions in the superintegrable chiral Potts spin chain |
| topic | Mathematical Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2603.27930 |