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

Walmsley Hagendorf, Christian; Rosengren, Hjalmar

doi:10.1007/s00220-024-04977-w

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

Walmsley Hagendorf, Christian

;

Rosengren, Hjalmar

(2024) Communications in Mathematical Physics — Vol. 405, p. Article 97 (2024)

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Authors

Walmsley Hagendorf, ChristianUCLouvain
Author
Rosengren, HjalmarChalmers University of Technology, University of Gothenburg
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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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UCLouvainSST/IRMP - Institut de recherche en mathématique et physique

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Walmsley Hagendorf, C., & Rosengren, H. (2024). Nearest-neighbour correlation functions for the supersymmetric XYZ spin chain and Painlevé VI. Communications in Mathematical Physics, 405, Article 97. https://doi.org/10.1007/s00220-024-04977-w (Original work published 2024)