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Reduced qKZ equation: general case

Klümper, A., Nirov, K., Razumov, A.

Published Jan 1, 2020• 6 citations
OpenAlex

Abstract

We use the quantum group approach for the investigation of correlation functions of integrable vertex models and spin chains. For the inhomogeneous reduced density matrix in case of an arbitrary simple Lie algebra we find functional equations of the form of the reduced quantum Knizhnik-Zamolodchikov equation. This equation is the starting point for the investigation of correlation functions at arbitrary temperature and notably for the ground state.

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We use the quantum group approach for the investigation of correlation functions of integrable vertex models and spin chains. For the inhomogeneous reduced density matrix in case of an arbitrary simple Lie algebra we find functional equations of the form of the reduced quantum Knizhnik-Zamolodchikov equation. This equation is the starting point for the investigation of correlation functions at arbitrary temperature and notably for the ground state.
We present a new approach to the static finite temperature correlation functions of the Heisenberg chain based on functional equations. An inhomogeneous generalization of the n -site density operator is considered. The lattice path integral formulation with a finite but arbitrary Trotter number allows us to derive a set of discrete functional equations with respect to the spectral parameters. We show that these equations yield a unique characterization of the density operator. Our functional equations are a discrete version of the reduced q-Knizhnik–Zamolodchikov equations which played a central role in the study of the zero temperature case. As a natural result, and independent of the arguments given by Jimbo et al (2009 J. Phys. A: Math. Theor. 42 304018), we prove that the inhomogeneous finite temperature correlation functions have the same remarkable structure as for zero temperature: they are a sum of products of nearest-neighbour correlators.