Elsevier

Nuclear Physics B

Volume 554, Issue 3, 16 August 1999, Pages 647-678
Nuclear Physics B

Form factors of the XXZ Heisenberg spin-12 finite chain☆

https://doi.org/10.1016/S0550-3213(99)00295-3Get rights and content

Abstract

Form factors for local spin operators of the XXZ Heisenberg spin-z finite chain are computed. Representation theory of Drinfel'd twists in terms of F-matrices for the quantum affine algebra Uq(ŝl2) in finite-dimensional modules is used to calculate scalar products of two states involving one Bethe state (leading to Gaudin formula) and to solve the quantum inverse problem for local spin operators in the finite chain. Hence, we obtain the representation of the n-spin correlation functions in terms of expectation values (in ferromagnetic reference state) of the operator entries of the quantum monodromy matrix satisfying Yang-Baxter algebra. This leads to the direct calculation of the form factors of the XXZ Heisenberg spin-! finite chain as determinants of usual functions of the parameters of the model. A two-point correlation function for adjacent sites is also derived using similar techniques.

References (49)

  • A.A. Belavin et al.

    Nucl. Phys. B

    (1984)
  • V.G. Knizhnik et al.

    Nucl. Phys. B

    (1984)
  • A.B. Zamolodchikov et al.

    Ann. Phys.

    (1979)
  • M. Jimbo

    Phys. Lett. A

    (1992)
  • R.J. Baxter

    Exactly Solved Models in Statistical Mechanics

    (1982)
  • L.D. Faddeev

    Les Houches 1982, Recent Advances in Field Theory and Statistical Mechanics

  • M. Gaudin

    La Fonction d'Onde de Bethe

    (1983)
  • F.A. Smirnov

    Form Factors in Completely Integrable Models of Quantum Field Theory

    (1992)
  • V.E. Korepin et al.

    Quantum Inverse Scattering Method and Correlation Functions

    (1993)
  • M. Jimbo et al.

    Algebraic Analysis of Solvable Lattice Models

    (1995)
  • C.N. Yang

    Phys. Rev.

    (1952)
  • T.T. Wu

    Phys. Rev. B

    (1976)
  • M. Sato et al.

    Publ. RIMS, Kyoto Univ.

    (1979)
  • A. Lenard

    J. Math. Phys.

    (1964)
  • A. Lenard

    J. Math. Phys.

    (1966)
  • L.D. Faddeev et al.

    Theor. Math. Phys.

    (1979)
  • V.G. Drinfel'd
  • M. Jimbo

    Lett. Math. Phys.

    (1985)
  • M. Jimbo

    Lett. Math. Phys.

    (1986)
  • L.D. Faddeev et al.

    Leningrad Math. J.

    (1990)
  • I.B. Frenkel et al.

    Commun. Math. Phys.

    (1992)
  • E. Date et al.

    Commun. Math. Phys.

    (1993)
  • M. Jimbo

    J. Phys. A

    (1994)
  • F.A. Smimov

    RIMS preprint 860

    (1992)

    • Cited by (0)

    ☆

    This work is supported by CNRS (France), the EC-TMR contract FMRX-CT96-0012, MAE fellowship 96/9804 and MENRT (France) fellowship AC 97-2-00119.

    4

    UMR 5672 du CNRS, associée a I'Ecole Normale Supérieure de Lyon.

    1

    On leave of absence from the St Petersburg branch of the Steklov Mathematical Institute, Fontanka 27, St Petersburg 191011, Russia.

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