Nearest-Neighbour Correlation Functions for the Supersymmetric XYZ Spin Chain and Painlevé VI

Abstract

AbstractWe 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 $$s_n$$ s n and $${{\bar{s}}}_n$$ s ¯ n introduced by Bazhanov and Mangazeev. Furthermore, we give an interpretation of the correlation functions in terms of the Painlevé VI Hamiltonian.