Abstract:
This paper is a continuation of our previous papers [4] and [5]. We discuss the new form of solution to the quantum Knizhnik–Zamolodchikov equation (qKZ) of level -4 obtained in [5] for the Heisenberg XXX spin chain in more detail. The main advantage of this form is that it explicitly reduces to one-dimensional integrals. We believe that the basic mathematical reason for this is some special cohomologies of deformed Jacobi varieties. We apply this new form of the solution to correlation functions by using the Jimbo–Miwa conjecture [7]. Formula (45) for correlation functions obtained in this way is in a good agreement with the ansatz for the emptiness formation probability from [4]. Our previous conjecture describing the structure of correlation functions of the XXX model in the homogeneous limit through the Riemann zeta functions at odd arguments is a corollary to (45).
Key words and phrases:
Exactly solvable models, correlation functions, quantum Knizhnik–Zamolodchikov equations.
Citation:
H. Boos, V. E. Korepin, F. A. Smirnov, “New formulae for solutions to quantum Knizhnik–Zamolodchikov equations of level −4 and correlation functions”, Mosc. Math. J., 4:3 (2004), 593–617
\Bibitem{BooKorSmi04}
\by H.~Boos, V.~E.~Korepin, F.~A.~Smirnov
\paper New formulae for solutions to quantum Knizhnik--Zamolodchikov equations of level $-4$ and correlation functions
\jour Mosc. Math.~J.
\yr 2004
\vol 4
\issue 3
\pages 593--617
\mathnet{http://mi.mathnet.ru/mmj165}
\crossref{https://doi.org/10.17323/1609-4514-2004-4-3-593-617}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2119141}
\zmath{https://zbmath.org/?q=an:1154.82305}
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Linking options:
https://www.mathnet.ru/eng/mmj165
https://www.mathnet.ru/eng/mmj/v4/i3/p593
This publication is cited in the following 4 articles:
Aufgebauer B., Kluemper A., “Finite Temperature Correlation Functions From Discrete Functional Equations”, J. Phys. A-Math. Theor., 45:34 (2012), 345203
Sato J., Aufgebauer B., Boos H., Goehmann F., Kluemper A., Takahashi M., Trippe Ch., “Computation of Static Heisenberg-Chain Correlators: Control over Length and Temperature Dependence”, Physical Review Letters, 106:25 (2011), 257201
Boos H.E., Goehmann F., Kluemper A., Suzuki J., “Factorization of the finite temperature correlation functions of the XXZ chain in a magnetic field”, Journal of Physics A-Mathematical and Theoretical, 40:35 (2007), 10699–10727
Boos H., Jimbo M., Miwa T., Smirnov F., Takeyama Y., “Reduced qKZ equation and correlation functions of the XXZ model”, Comm. Math. Phys., 261:1 (2006), 245–276