Correlation functions of the integrable $SU(n)$ spin chain

Abstract

We study the correlation functions of $SU(n)$ $n>2$ invariant spin chains in the thermodynamic limit. We formulate a consistent framework for the computation of short-range correlation functions via functional equations which hold even at finite temperature. We give the explicit solution for two- and three-site correlations for the $SU(3)$ case at zero temperature. The correlators do not seem to be of factorizable form. From the two-sites result we see that the correlation functions are given in terms of Hurwitz' zeta function, which differs from the $SU(2)$ case where the correlations are expressed in terms of Riemann's zeta function of odd arguments.

44 pages, 11 figures

References in corpus (4)

• Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions
• Factorization of the finite temperature correlation functions of the XXZ chain in a magnetic field
• Finite temperature correlation functions from discrete functional equations
• Correlation functions of the integrable isotropic spin-1 chain at finite temperature

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• Vertex Models and Spin Chains in Formulas and Pictures
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• The LeClair-Mussardo series and nested Bethe Ansatz
• On correlation functions in models related to the Temperley-Lieb algebra
• On the properties of the density matrix of the ${\mathfrak{sl}}_{n+1}$-invariant model