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Asymptotic expansions for correlation functions of one-dimensional bosons

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Abstract

We discuss different asymptotic representations for correlation functions of critical integrable systems. We prove that in the one-dimensional boson model, the asymptotic series for correlation functions obtained by the multiple-integral method coincides with the conformal field theory predictions in the low-temperature limit.

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References

  1. K. K. Kozlowski, J. M. Maillet, and N. A. Slavnov, J. Stat. Mech., 1103, P03018 (2011).

    Article  Google Scholar 

  2. K. K. Kozlowski, J. M. Maillet, and N. A. Slavnov, J. Stat. Mech., 1103, P03019 (2011).

    Article  Google Scholar 

  3. N. Kitanine, K. K. Kozlowski, J. M. Maillet, N. A. Slavnov, and V. Terras, J. Stat. Mech., 1112, P12010 (2011); arXiv:1110.0803v2 [hep-th] (2011).

    Article  Google Scholar 

  4. A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, Nucl. Phys. B, 241, 333–380 (1984).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. J. L. Cardy, J. Phys. A, 17, L385–L387 (1984).

    Article  MathSciNet  ADS  Google Scholar 

  6. J. L. Cardy, Nucl. Phys. B, 270, 186–204 (1986).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. H. Bethe, Z. Phys., 71, 205–226 (1931).

    Article  ADS  Google Scholar 

  8. R. Orbach, Phys. Rev., 112, 309–316 (1958).

    Article  ADS  Google Scholar 

  9. E. H. Lieb and W. Liniger, Phys. Rev., 130, 1605–1616 (1963).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. E. H. Lieb and D. C. Mattis, Mathematical Physics in One Dimension, Acad. Press, New York (1966).

    Google Scholar 

  11. H. J. de Vega and F. Woynarovich, Nucl. Phys. B, 251, 439–456 (1985).

    Article  ADS  Google Scholar 

  12. H. W. Blöte, J. L. Cardy, and M. P. Nightingale, Phys. Rev. Lett., 56, 742–745 (1986).

    Article  ADS  Google Scholar 

  13. I. Affleck, Phys. Rev. Lett., 56, 745–748 (1986).

    MathSciNet  ADS  Google Scholar 

  14. N. M. Bogolyubov, A. G. Izergin, and N. Yu. Reshetikhin, JETP Lett., 44, 521–523 (1986).

    MathSciNet  ADS  Google Scholar 

  15. A. Berkovich and G. Murthy, J. Phys. A, 21, L395–L400 (1988).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. A. Berkovich and G. Murthy, J. Phys. A, 21, 3703–3721 (1988).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. A. Klümper and M. Batchelor, J. Phys. A, 23, L189–L195 (1990).

    Article  ADS  MATH  Google Scholar 

  18. A. Klümper, M. Batchelor, and P. Pearce, J. Phys. A, 24, 3111–3133 (1991).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. A. Klümper, Z. Phys. B, 91, 507–519 (1993); arXiv:cond-mat/9306019v1 (1993).

    Article  ADS  Google Scholar 

  20. A. Klümper, T. Wehner, and J. Zittartz, J. Phys. A, 26, 2815–2827 (1993).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. A. Klümper, “Integrability of quantum chains: Theory and applications to the spin-1/2 XXZ chain,” in: Quantum Magnetism (Lect. Notes Phys., Vol. 645, U. Schollwock, J. Richter, D. J. J. Farnell, and R. F. Bishop, eds.), Springer, Berlin (2004), pp. 349–379; arXiv:cond-mat/0502431v1 (2005).

    Chapter  Google Scholar 

  22. A. Seel, T. Bhattacharyya, F. Göhmann, and A. Klümper, J. Stat. Mech., 0708, P08030 (2007).

    Article  Google Scholar 

  23. C. N. Yang and C. P. Yang, J. Math. Phys., 10, 1115–1122 (1969).

    Article  ADS  MATH  Google Scholar 

  24. C. P. Yang, Phys. Rev. A, 2, 154–157 (1970).

    Article  ADS  Google Scholar 

  25. M. Takahashi, Prog. Theoret. Phys., 46, 401–415 (1971).

    Article  ADS  Google Scholar 

  26. M. Gaudin, Phys. Rev. Lett., 26, 1301–1304 (1971).

    Article  ADS  Google Scholar 

  27. E. K. Sklyanin, L. A. Takhtadzhyan, and L. D. Faddeev, Theor. Math. Phys., 40, 688–706 (1979).

    Article  MathSciNet  Google Scholar 

  28. L. D. Faddeev, “How algebraic Bethe ansatz works for integrable models,” in: Symétries quantiques (Les Houches, 1 August-8 September 1995, A. Connes, K. Gawedzki, and J. Zinn-Justin, eds.), North-Holland, Amsterdam (1998), pp. 149–219.

    Google Scholar 

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

    Book  MATH  Google Scholar 

  30. N. M. Bogolyubov and V. E. Korepin, Theor. Math. Phys., 60, 808–814 (1984).

    Article  MathSciNet  Google Scholar 

  31. N. M. Bogoliubov, A. G. Izergin, and V. E. Korepin, “Quantum inverse scattering method and correlation functions,” in: Exactly Solvable Problems in Condensed Matter and Relativistic Field Theory (Lect. Notes Phys., Vol. 242, B. S. Shastry, S. S. Jha, and V. Singh, eds.), Springer, Berlin (1985), pp. 220–316.

    Chapter  Google Scholar 

  32. J. D. Johnson and B. M. McCoy, Phys. Rev. A, 6, 1613–1626 (1972).

    Article  ADS  Google Scholar 

  33. L. Mezincescu and R. I. Nepomechie, “Introduction to the thermodynamics of spin chains,” in: Quantum Groups, Integrable Models, and Statistical Systems (Kingston, Canada, 13–17 July 1992, J. LeTourneux and L. Vinet, eds.), World Scientific, Singapore (1993), pp. 168–191; arXiv:hep-th/9212124v1 (1992).

    Google Scholar 

  34. N. A. Slavnov, Theor. Math. Phys., 121, 1358–1376 (1999).

    Article  MathSciNet  MATH  Google Scholar 

  35. S. V. Kerov, Funct. Anal. Appl., 34, No. 1, 41–51 (2000).

    Article  MathSciNet  MATH  Google Scholar 

  36. A. Borodin and G. Olshanski, Electron. J. Combin., 7, R28 (2000).

    MathSciNet  Google Scholar 

  37. A. Borodin and G. Olshanski, Commun. Math. Phys., 211, 335–358 (2000); arXiv:math/9904010v1 (1999).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  38. A. Okounkov, “SL(2) and z-measures,” in: Random Matrix Models and Their Applications (Math. Sci. Res. Inst. Publ., Vol. 40, P. Bleher and A. Its, eds.), Cambridge Univ. Press, Cambridge (2001), pp. 407–420.

    Google Scholar 

  39. N. Kitanine, K. K. Kozlowski, J. M. Maillet, N. A. Slavnov, and V. Terras, J. Stat. Mech., 1105, P05028 (2011).

    Article  Google Scholar 

  40. N. Kitanine, K. K. Kozlowski, J. M. Maillet, N. A. Slavnov, and V. Terras, J. Math. Phys., 50, 095209 (2009); arXiv:0903.2916v1 [hep-th] (2009).

    Article  MathSciNet  ADS  Google Scholar 

  41. N. Kitanine, K. K. Kozlowski, J. M. Maillet, N. A. Slavnov, and V. Terras, J. Stat. Mech., 0701, P01022 (2007).

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Steklov Mathematical Institute, RAS, Moscow, Russia

    N. A. Slavnov

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  1. N. A. Slavnov
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Correspondence to N. A. Slavnov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 174, No. 1, pp. 125–139, January, 2013.

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Slavnov, N.A. Asymptotic expansions for correlation functions of one-dimensional bosons. Theor Math Phys 174, 109–121 (2013). https://doi.org/10.1007/s11232-013-0009-1

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