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Determinant Representations of Correlation Functions for the Supersymmetric t-J Model

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Abstract

Working in the F-basis provided by the factorizing F-matrix, the scalar products of Bethe states for the supersymmetric t-J model are represented by determinants. By means of these results, we obtain determinant representations of correlation functions for the model.

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References

  1. Smirnov F.A. (1992) Form Factors in Completely Integrable Models of Quantum Field Theory. Singapore, World Scientific

    MATH  Google Scholar 

  2. Korepin V.E., Bogoliubov N.M., Izergin A.G. (1993) Quantum Inverse Scattering Method and Correlation Functions. Cambridge, Cambridge Univ. Press

    MATH  Google Scholar 

  3. Frenkel I.B., Reshetikhin N.Y. (1992) Quantum affine algebras and holonomic difference equations. Commun. Math. Phys. 146, 1

    Article  MATH  ADS  MathSciNet  Google Scholar 

  4. Davies B., Foda O., Jimbo M., Miwa T., Nakayashiki A. (1993) Diagonalization of the XXZ Hamiltonian by vertex operators. Commun. Math. Phys. 151, 89

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. Koyama Y. (1994) Staggered polarization of vertex models with \(U_q(\widehat{{sl}(n)})\)-symmetry. Commun. Math. Phys. 164, 277

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. Jimbo M., Miwa T. (1995) Algebraic analysis of solvable Lattice models. Providence, RI AMS

    MATH  Google Scholar 

  7. Yang W.-L., Zhang Y.Z. (1999) Highest weight representations of \(U_q(\widehat{sl(2|1))}\) and correlation functions of q-deformed supersymmetric t-J model. Nucl. Phys. B 547, 599

    MATH  Google Scholar 

  8. Hou B.Y., Yang W.-L., Zhang Y.Z. (1999) The twisted quantum affine algebra \(U_q(A^{(2)}_2)\) and the correlation functions of the Izergin-Korepin model. Nucl. Phys. B 556, 485

    MATH  MathSciNet  Google Scholar 

  9. Korepin V.E. (1982) Calculation of the norms of the Bethe wave functions. Commun. Math. Phys. 86, 391

    Article  MATH  ADS  MathSciNet  Google Scholar 

  10. Izergin A.G. (1987) Partition function of the 6-vertex model in a finite volume. Sov. Phys. Dokl. 32, 878

    ADS  Google Scholar 

  11. Maillet, J.M., Sanchez de Santos, I.: Drinfel’d twists and algebraic Bethe ansatz. http://arxiv.org/q-alg/9612012, 1996

  12. Kitanine N., Maillet J.M., Terras V. (1999) Form factors of the XXZ Heisenberg spin-1/2 finite chain. Nucl. Phys. B 554, 647

    MATH  MathSciNet  Google Scholar 

  13. Yang W.-L., Zhang Y.-Z., Zhao S.-Y. (2004) Drinfeld twists and algebraic Bethe ansatz of the supersymmetric t-J model. JHEP 12, 038

    Article  ADS  MathSciNet  Google Scholar 

  14. Zhao, S.-Y., Yang, W.-L., Zhang, Y.-Z.: Drinfeld twists and symmetric Bethe vectors of supersymmetric Fermion models. J. Stat. Mech., P04005 (2005)

  15. Yang W.-L., Zhang Y.-Z., Zhao S.-Y. (2006) Drinfeld twists and algebraic Bethe ansatz of the quantum supersymmetric model associated with U q (gl(m|n)). Commun. Math. Phys. 264(1): 87–114

    Article  MATH  ADS  MathSciNet  Google Scholar 

  16. Zhao S.-Y., Yang W.-L., Zhang Y.-Z. (2006) Determinant representation of correlation functions for the U q (gl(1|1)) free Fermion model. J. Math. Phys. 47, 013302

    Article  ADS  MathSciNet  Google Scholar 

  17. Perk J.H.H., Schultz C.L. (1981) New families of commuting transfer matrices in q-state vertex models. Phys. Lett. A 84, 407

    Article  ADS  MathSciNet  Google Scholar 

  18. Kulish P.P., Sklyanin E.K. (1982) On solutions of the Yang-Baxter equation. J. Soviet Math. 19: 1596

    Article  MATH  Google Scholar 

  19. Kulish P.P. (1986) Integrable graded magnets. J. Soviet Math. 35: 2648

    Article  MATH  Google Scholar 

  20. Sutherland B. (1975) Model for a multicomponent quantum system. Phys. Rev. B 12: 3795

    Article  ADS  Google Scholar 

  21. Schultz C.L. (1983) Eigenvectors of the multi-component generalization of the six-vertex model. Physica A 122: 71

    Article  ADS  MathSciNet  Google Scholar 

  22. Wiegmann P.B. (1988) Superconductivity in strongly correlated electronic systems and confinement versus deconfinement phenomenon. Phys. Rev. Lett. 60: 821

    Article  ADS  Google Scholar 

  23. Anderson P.W. (1990) Singular forward scattering in the 2D Hubbard model and a renormalized Bethe ansatz ground state. Phys. Rev. Lett. 65: 2306

    Article  ADS  Google Scholar 

  24. Essler F.H.L., Korepin V.E. (1992) Higher conservation laws and algebraic Bethe ansatz for the supersymmetric t-J model. Phys. Rev. B 46: 9147

    Article  Google Scholar 

  25. Foerster A., Karowski M. (1993) Algebraic properties of the Bethe ansatz for an spl(2,1)-supersymmetric t-J model. Nucl. Phys. B 396, 611

    MathSciNet  Google Scholar 

  26. Ambjorn J., Arnaudon D., Sedrakyan A., Sedrakyan T., Sorba P (2001) Integrable ladder t-J model with staggered shift of the spectral parameter. J. Phys. A 34: 5887

    MATH  MathSciNet  Google Scholar 

  27. Albert T.-D., Boos H., Flume R., Ruhlig K. (2000) Resolution of the nested hierarchy for the rational sl(n) models. J. Phys. A 33: 4963

    Article  MATH  ADS  MathSciNet  Google Scholar 

  28. Göhmann F., Korepin V.E. (2000) Solution of the quantum inverse problem, J. Phys. A 33: 1199

    Article  MATH  ADS  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Queensland, Brisbane, QLD, 4072, Australia

    Shao-You Zhao, Wen-Li Yang & Yao-Zhong Zhang

  2. Department of Physics, Beijing Institute of Technology, Beijing, 100081, China

    Shao-You Zhao

  3. Institute of Modern Physics, Northwest University, Xian, 710069, P.R. China

    Wen-Li Yang

Authors
  1. Shao-You Zhao
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  2. Wen-Li Yang
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  3. Yao-Zhong Zhang
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Correspondence to Shao-You Zhao.

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Communicated by L. Takhtajan

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Zhao, SY., Yang, WL. & Zhang, YZ. Determinant Representations of Correlation Functions for the Supersymmetric t-J Model. Commun. Math. Phys. 268, 505–541 (2006). https://doi.org/10.1007/s00220-006-0113-2

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  • DOI: https://doi.org/10.1007/s00220-006-0113-2

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