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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

A recursion formula for the correlation functions of an inhomogeneous XXX model


Authors: H. Boos, M. Jimbo, T. Miwa, F. Smirnov and Y. Takeyama
Original publication: Algebra i Analiz, tom 17 (2005), nomer 1.
Journal: St. Petersburg Math. J. 17 (2006), 85-117
MSC (2000): Primary 82B23
Published electronically: January 23, 2006
MathSciNet review: 2140676
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Abstract | References | Similar Articles | Additional Information

Abstract: A new recursion formula is presented for the correlation functions of the integrable spin $ 1/2$ XXX chain with inhomogeneity. It links the correlators involving $ n$ consecutive lattice sites to those with $ n-1$ and $ n-2$ sites. In a series of papers by V. Korepin and two of the present authors, it was discovered that the correlators have a certain specific structure as functions of the inhomogeneity parameters. The formula mentioned above makes it possible to prove this structure directly, as well as to obtain an exact description of the rational functions that were left undetermined in the earlier work.


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Additional Information

H. Boos
Affiliation: Physics Department, University of Wuppertal, D-42097, Wuppertal, Germany, and Institute for High Energy Physics, Protvino 142284, Russia
Email: boos@physik.uni-wuppertal.de

M. Jimbo
Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, Tokyo 153-8914, Japan
Email: jimbomic@ms.u-tokyo.ac.jp

T. Miwa
Affiliation: Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
Email: tetsuji@math.kyoto-u.ac.jp

F. Smirnov
Affiliation: (Membre du CNRS): Laboratoire de Physique Théorique et Hautes Energies, Université Pierre et Marie Curie, Tour 16 1$^{er}$ étage, 4 Place Jussieu, 75252 Paris Cedex 05, France
Email: smirnov@lpthe.jussieu.fr

Y. Takeyama
Affiliation: Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8571, Japan
Email: takeyama@math.tsukuba.ac.jp

DOI: http://dx.doi.org/10.1090/S1061-0022-06-00894-6
PII: S 1061-0022(06)00894-6
Keywords: Exactly solvable models, spin chains, correlation functions
Received by editor(s): October 9, 2004
Published electronically: January 23, 2006
Additional Notes: Research of H. Boos was supported by INTAS grant #00–00561 and by RFBR grant #04–01–00352.
Research of M. Jimbo was partially supported by the Grant-in-Aid for Scientific Research B2–16340033.
Research of T. Miwa was partially supported by the Grant-in-Aid for Scientific Research A1–13304010.
Research of F. Smirnov was supported by INTAS grant #00–00055 and by the EC network “EUCLID”, contract number HPRN–CT–2002–00325.
Research of Y. Takeyama was partially supported by the University of Tsukuba Research Project.
This work was started during the workshop, 21COE RIMS Research Project 2004, Quantum Integrable Systems and Infinite-Dimensional Algebras, February 4–24, 2004.
Dedicated: Dedicated to Ludwig Faddeev on the occasion of his seventieth birthday
Article copyright: © Copyright 2006 American Mathematical Society