The $XX$ and Ising Limits in Integral Formulas for Finite-Temperature Correlation Functions of the $XXZ$ Chain
Teoretičeskaâ i matematičeskaâ fizika, Tome 146 (2006) no. 1, pp. 146-160 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a multiple-integral representation for a one-parameter generating function of the finite temperature $S^z$$S^z$ correlation functions of the antiferromagnetic spin-$1/2$ $XXZ$ chain in the $XX$ limit and in the Ising limit. We show how the multiple integrals reduce to single integrals in these limits, thus reproducing known results.
Keywords: quantum spin chain, exact finite-temperature correlation functions, $XX$ model.
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     title = {The $XX$ and {Ising} {Limits} in {Integral} {Formulas} for {Finite-Temperature} {Correlation} {Functions} of the $XXZ$ {Chain}},
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F. Gohmann; A. Seel. The $XX$ and Ising Limits in Integral Formulas for Finite-Temperature Correlation Functions of the $XXZ$ Chain. Teoretičeskaâ i matematičeskaâ fizika, Tome 146 (2006) no. 1, pp. 146-160. http://geodesic.mathdoc.fr/item/TMF_2006_146_1_a11/

[1] M. Jimbo, K. Miki, T. Miwa, A. Nakayashiki, Phys. Lett. A, 168 (1992), 256 ; M. Jimbo, T. Miwa, J. Phys. A, 29 (1996), 2923 | DOI | MR | DOI | MR | Zbl

[2] N. Kitanine, J. M. Maillet, V. Terras, Nucl. Phys. B, 567 (2000), 554 | DOI | MR | Zbl

[3] H. E. Boos, V. E. Korepin, J. Phys. A, 34 (2001), 5311 | DOI | MR | Zbl

[4] H. E. Boos, V. E. Korepin, F. A. Smirnov, Nucl. Phys. B, 658 (2003), 417 | DOI | MR | Zbl

[5] H. Boos, M. Jimbo, T. Miwa, F. Smirnov, Y. Takeyama, A recursion formula for the correlation functions of an inhomogeneous XXX model, hep-th/0405044 | MR

[6] G. Kato, M. Shiroishi, M. Takahashi, K. Sakai, J. Phys. A, 36 (2003), L337 ; 37 (2004), 5097 | DOI | MR | Zbl | DOI | MR | Zbl

[7] N. Kitanine, J. M. Maillet, N. A. Slavnov, V. Terras, Nucl. Phys. B, 641 (2002), 487 | DOI | MR | Zbl

[8] N. Kitanine, J. M. Maillet, N. A. Slavnov, V. Terras, J. Phys. A, 38 (2005), 7441 ; hep-th/0407223 | DOI | MR | Zbl

[9] N. Kitanine, J. M. Maillet, N. A. Slavnov, V. Terras, Dynamical correlation functions of the $XXZ$ spin-1/2 chain, hep-th/0407108 | MR

[10] A. Klümper, Ann. Phys. (Leipzig), 1 (1992), 540 ; Z. Phys. B, 91 (1993), 507 | DOI | DOI

[11] M. Inoue, M. Suzuki, Prog. Theor. Phys., 79 (1988), 645 ; M. Suzuki, Phys. Rev. B, 31 (1985), 2957 | DOI | MR | DOI

[12] F. Göhmann, A. Klümper, A. Seel, J. Phys. A, 37 (2004), 7625 | DOI | MR | Zbl

[13] F. Göhmann, A. Klümper, A. Seel, Physica B, 359–361 (2004), 807 ; cond-mat/0406611 | DOI | MR

[14] F. Göhmann, A. Klümper, A. Seel, J. Phys. A, 38 (2005), 1833 | DOI | MR | Zbl

[15] Z. Tsuboi, M. Shiroishi, J. Phys. A, 38 (2005), L363 ; cond-mat/0502569 | DOI | MR | Zbl

[16] M. Bortz, F. Göhmann, Eur. Phys. J. B, 46 (2005), 399 ; cond-mat/0504370 | DOI

[17] N. Kitanine, J. M. Maillet, N. A. Slavnov, V. Terras, Nucl. Phys. B, 642 (2002), 433 | DOI | MR | Zbl

[18] A. G. Izergin, V. E. Korepin, Commun. Math. Phys., 94 (1984), 67 | DOI | MR | Zbl

[19] M. Shiroishi, M. Takahashi, Y. Nishiyama, J. Phys. Soc. Japan, 70 (2001), 3535 | DOI | Zbl

[20] E. H. Lieb, T. Schultz, D. Mattis, Ann. Physics (N.Y.), 16 (1961), 407 | DOI | MR | Zbl

[21] E. Barouch, B. M. McCoy, Phys. Rev. A, 3 (1971), 786 | DOI

[22] M. Suzuki, Phys. Lett. A, 301 (2002), 398 | DOI | Zbl

[23] R. Bekster, Tochno reshaemye modeli v statisticheskoi mekhanike, M., Mir, 1985 | MR