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

2022/08/29 by Christian Hagendorf, Hjalmar Rosengren, Hagendorf, Christian +1
Chemistry · Mathematics · #Algebraic structures and combinatorial models #Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2208.13533

openalex publication_date 2022/08/29 · openalex created_date 2022/08/31 · openalex updated_date 2026/07/28

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 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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