Geodesic
Creation operators for the Fateev–Zamolodchikov spin chain
Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 1, pp. 45-72 Cet article a éte moissonné depuis la source Math-Net.Ru

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In previous works, we studied the problem of constructing a basis in the space of local operators for an anisotropic XXZ spin chain with spin $1/2$ such that the vacuum expectation values have a simple form. For this, we introduced fermionic creation operators. Here, we extend this construction to the spin-$1$ case. Using a certain version of the fusion procedure, we find two doublets of fermionic creation operators and one triplet of bosonic creation operators. We prove that the basis obtained by the action of these operators satisfies the dual reduced quantum Knizhnik–Zamolodchikov equation.
Keywords: exactly solvable model, Heisenberg magnet, correlation function. 
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M. Jimbo; T. Miwa; F. A. Smirnov. Creation operators for the Fateev–Zamolodchikov spin chain. Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 1, pp. 45-72. http://geodesic.mathdoc.fr/item/TMF_2014_181_1_a3/

[1] H. Boos, V. Korepin, J. Phys. A, 34:26 (2001), 5311–5316 | DOI | MR | Zbl

[2] H. E. Boos, V. E. Korepin, “Evaluation of integrals representing correlations in $XXX$ Heisenberg spin chain”, MathPhys Odyssey 2001, Progress in Mathematical Physics, 23, eds. M. Kashiwara, T. Miwa, Birkhäuser, Boston, MA, 2002, 65–108 | MR | Zbl

[3] M. Jimbo, T. Miwa, Algebraic Analysis of Solvable Lattice Models, CBMS Regional Conference Series in Mathematics, 85, AMS, Providence, RI, 1995 | MR | Zbl

[4] N. Kitanine, J.-M. Maillet, V. Terras, Nucl. Phys. B, 567:3 (2000), 554–582 | DOI | MR | Zbl

[5] H. E. Boos, V. E. Korepin, F. A. Smirnov, Nucl. Phys. B, 658:3 (2003), 417–439 | DOI | MR | Zbl

[6] H. Boos, M. Jimbo, T. Miwa, F. Smirnov, Y. Takeyama, Algebra i analiz, 17:1 (2005), 115–159 | DOI | MR | Zbl

[7] H. Boos, M. Jimbo, T. Miwa, F. Smirnov, Y. Takeyama, Commun. Math. Phys., 261:1 (2006), 245–276 | DOI | MR | Zbl

[8] H. Boos, M. Jimbo, T. Miwa, F. Smirnov, Y. Takeyama, Commun. Math. Phys., 272:1 (2007), 263–281 | DOI | MR | Zbl

[9] H. Boos, M. Jimbo, T. Miwa, F. Smirnov, Y. Takeyama, Commun. Math. Phys., 286:3 (2009), 875–932 | DOI | MR | Zbl

[10] M. Jimbo, T. Miwa, F. Smirnov, J. Phys. A, 42:30 (2009), 304018, 31 pp. | DOI | MR | Zbl

[11] M. Rigol, V. Dunjko, V. Yurovsky, M. Olshanii, Phys. Rev. Lett., 98:5 (2007), 050405, 4 pp. | DOI

[12] H. Boos, M. Jimbo, T. Miwa, F. Smirnov, Commun. Math. Phys., 299:3 (2010), 825–866 | DOI | MR | Zbl

[13] M. Jimbo, T. Miwa, F. Smirnov, “On one-point functions of descendants in sine-Gordon model”, New Trends in Quantum Integrable Systems (Kyoto, Japan, 27–31 July, 2009), eds. B. Feigin, M. Jimbo, M. Okado, World Sci., Singapore, 2010, 117–137 | DOI | MR

[14] M. Jimbo, T. Miwa, F. Smirnov, Lett. Math. Phys., 96:1–3 (2011), 325–365 | DOI | MR | Zbl

[15] Al. Zamolodchikov, Nucl. Phys. B, 348:3 (1991), 619–641 | DOI | MR

[16] S. Negro, F. Smirnov, Reflection equation and fermionic basis, arXiv: 1304.1860

[17] S. Negro, F. Smirnov, Nucl. Phys. B, 875:1 (2013), arXiv: 1306.1476 | DOI | MR | Zbl

[18] V. Fateev, D. Fradkin, S. Lukyanov, A. Zamolodchikov, Al. Zamolodchikov, Nucl. Phys. B, 540:3 (1999), 587–609 | DOI | MR | Zbl

[19] A. B. Zamolodchikov, V. A. Fateev, YaF, 32:2 (1980), 581–590 | MR

[20] N. Kitanine, J. Phys. A, 34:39 (2001), 8151–8169 | DOI | MR | Zbl

[21] A. Klümper, D. Nawrah, J. Suzuki, Correlation functions of the integrable isotropic spin-1 chain: algebraic expressions for arbitrary temperature, arXiv: 1304.5512

[22] H. Boos, M. Jimbo, T. Miwa, F. Smirnov, Y. Takeyama, PoS, 2007, 015, 34 pp.

[23] M. Jimbo, T. Miwa, F. Smirnov, “Fermions acting on quasi-local operators in the $XXZ$ model”, Symmetries, Integrable Systems and Representations (Tokyo, Japan, July 25–29, 2011), Springer Proceedings in Mathematics and Statistics, 40, eds. K. Iohara, S. Morier-Genoud, B. Remy, Springer, Heidelberg, 2013, 243–261 | DOI | MR | Zbl

[24] F. Smirnov, Form Factors in Completely Integrable Models of Quantum Field Theory, Advanced Series in Mathematical Physics, 14, World Sci., Singapore, 1992 | DOI | MR | Zbl