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arXiv · 2208.13533

Nearest-neighbour correlation functions for the supersymmetric XYZ spin chain and Painlevé VI

Christian Hagendorf·Hjalmar Rosengren
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Abstract

We study nearest-neighbour correlation functions for the ground state of the supersymmetric XYZ spin chain with odd length and periodic boundary conditions. Under a technical assumption related to the $Q$-operator of the corresponding eight-vertex model, we show that they can be expressed exactly in terms of the Painlevé VI tau functions $s_n$ and $\bar s_n$ introduced by Bazhanov and Mangazeev. Furthermore, we give an interpretation of the correlation functions in terms of the Painlevé VI Hamiltonian.

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Christian Hagendorf, Hjalmar Rosengren. 2022-08-29. Nearest-neighbour correlation functions for the supersymmetric XYZ spin chain and Painlevé VI. https://arxiv.org/abs/2208.13533

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