@article{TMF_2023_217_1_a9,
author = {G. Kulkarni and N. A. Slavnov},
title = {Scalar products of {Bethe} vectors in the~generalized algebraic},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {179--203},
year = {2023},
volume = {217},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2023_217_1_a9/}
}
G. Kulkarni; N. A. Slavnov. Scalar products of Bethe vectors in the generalized algebraic. Teoretičeskaâ i matematičeskaâ fizika, Tome 217 (2023) no. 1, pp. 179-203. http://geodesic.mathdoc.fr/item/TMF_2023_217_1_a9/
[1] E. K. Sklyanin, L. A. Takhtadzhyan, L. D. Faddeev, “Kvantovyi metod obratnoi zadachi. I”, TMF, 40:2 (1979), 194–220 | DOI | MR
[2] L. A. Takhtadzhyan, L. D. Faddeev, “Kvantovyi metod obratnoi zadachi i $XYZ$ model Geizenberga”, UMN, 34:5(209) (1979), 13–63 | DOI | MR
[3] L. D. Faddeev, “How the algebraic Bethe ansatz works for integrable models”, Symmétries quantiques [Quantum Symmetries], Proceedings of the Les Houches Summer School, Session LXIV (Les Houches, France, August 1 – September 8, 1995), eds. A. Connes, K. Gawedzki, J. Zinn-Justin, North-Holland, Amsterdam, 1998, 149–219, arXiv: hep-th/9605187 | MR | Zbl
[4] A. G. Izergin, V. E. Korepin, “The quantum inverse scattering method approach to correlation functions”, Commun. Math. Phys., 94:1 (1984), 67–92 | DOI | MR | Zbl
[5] V. E. Korepin, “Dual field formulation of quantum integrable models”, Commun. Math. Phys., 113:2 (1987), 177–190 | DOI | MR
[6] T. Kojima, V. E. Korepin, N. A. Slavnov, “Determinant representation for dynamical correlation function of the quantum nonlinear Schrödinger equation”, Commun. Math. Phys., 188:3 (1997), 657–689, arXiv: hep-th/9611216 | DOI | MR
[7] M. Jimbo, K. Miki, T. Miwa, A. Nakayashiki, “Correlation functions of the $XXZ$ model for $\Delta-1$”, Phys. Lett. A, 168:4 (1992), 256–263, arXiv: hep-th/9205055 | DOI | MR
[8] N. Kitanine, J. M. Maillet, V. Terras, “Correlation functions of the $XXZ$ Heisenberg spin-$1/2$ chain in a magnetic field”, Nucl. Phys. B, 567:3 (2000), 554–582, arXiv: math-ph/9907019 | DOI | MR | Zbl
[9] F. Göhmann, A. Klümper, A. Seel, “Integral representations for correlation functions of the $XXZ$ chain at finite temperature”, J. Phys. A: Math. Gen., 37:31 (2004), 7625–7652, arXiv: hep-th/0405089 | DOI | MR
[10] N. Kitanine, J. M. Maillet, N. A. Slavnov, V. Terras, “Master equation for spin-spin correlation functions of the $XXZ$ chain”, Nucl. Phys. B, 712:3 (2005), 600–622, arXiv: ; N. Kitanine, K. K. Kozlowski, J. M. Maillet, N. A. Slavnov, V. Terras, “Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions”, J. Stat. Mech., 2009:4 (2009), P04003, 66 pp., arXiv: ; “A form factor approach to the asymptotic behavior of correlation functions”, 2011:12 (2011), P12010, 28 pp., arXiv: ; “Form factor approach to dynamical correlation functions in critical models”, 2012:9 (2012), P09001, 33 pp., arXiv: hep-th/04061900808.02271110.08031206.2630 | DOI | MR | DOI | MR | DOI | DOI | MR
[11] J. S. Caux, J. M. Maillet, “Computation of dynamical correlation functions of Heisenberg chains in a magnetic field”, Phys. Rev. Lett., 95:7 (2005), 077201, 3 pp., arXiv: cond-mat/0502365 | DOI
[12] R. G. Pereira, J. Sirker, J. S. Caux, R. Hagemans, J. M. Maillet, S. R. White, I. Affleck, “Dynamical spin structure factor for the anisotropic spin-$1/2$ Heisenberg chain”, Phys. Rev. Lett., 96:25 (2006), 257202, 4 pp., arXiv: ; “Dynamical structure factor at small $q$ for the $XXZ$ spin-$1/2$ chain”, J. Stat. Mech., 2007:8 (2007), P08022, 64 pp., arXiv: cond-mat/06036810706.4327 | DOI | DOI | MR
[13] J. S. Caux, P. Calabrese, N. A. Slavnov, “One-particle dynamical correlations in the one-dimensional Bose gas”, J. Stat. Mech., 2007:1 (2007), P01008, 21 pp., arXiv: cond-mat/0611321 | DOI
[14] V. E. Korepin, N. M. Bogoliubov, A. G. Izergin, Quantum Inverse Scattering Method and Correlation Functions, Cambridge Univ. Press, Cambridge, 1993 | MR
[15] N. A. Slavnov, Algebraic Bethe Ansatz and Correlation Functions: An Advanced Course, World Sci., Singapore, 2022 | DOI | MR
[16] W. Heisenberg, “Zur Theorie des Ferromagnetismus”, Z. Phys., 49:9–10 (1928), 619–636 | DOI
[17] B. Sutherland, “Two-dimensional hydrogen bonded crystals without the ice rule”, J. Math. Phys., 11:11 (1970), 3183–3186 | DOI
[18] C. Fan, F. Y. Wu, “General lattice model of phase transitions”, Phys. Rev. B, 2:3 (1970), 723–733 | DOI
[19] R. J. Baxter, “Eight-vertex model in lattice statistics”, Phys. Rev. Lett., 26:14 (1971), 832–833 | DOI
[20] R. Bekster, Tochno reshaemye modeli v statisticheskoi mekhanike, Mir, M., 1985 | MR | MR | Zbl
[21] S. Belliard, N. A. Slavnov, “Why scalar products in the algebraic Bethe ansatz have determinant representation”, JHEP, 10 (2019), 103, 16 pp., arXiv: 1908.00032 | DOI | MR
[22] N. Slavnov, A. Zabrodin, A. Zotov, “Scalar products of Bethe vectors in the 8-vertex model”, JHEP, 06 (2020), 123, 53 pp., arXiv: 2005.11224 | DOI | MR
[23] N. Kitanine, J.-M. Maillet, V. Terras, “Form factors of the XXZ Heisenberg spin-$1/2$ finite chain”, Nucl. Phys. B, 554:3 (1999), 647–678, arXiv: math-ph/9807020 | DOI | MR
[24] F. Göhmann, V. E. Korepin, “Solution of the quantum inverse problem”, J. Phys. A: Math. Gen., 33:6 (2000), 1199–1220, arXiv: hep-th/9910253 | DOI | MR
[25] J. M. Maillet, V. Terras, “On the quantum inverse scattering problem”, Nucl. Phys. B, 575:3 (2000), 627–644, arXiv: hep-th/9911030 | DOI | MR
[26] G. Kulkarni, N. A. Slavnov, “Deistviya elementov matritsy monodromii v obobschennom algebraicheskom anzatse Bete”, prinyato k publikatsii, TMF, arXiv: 2303.02439
[27] E. Lieb, T. Schultz, D. Mattis, “Two soluble models of an antiferromagnetic chain”, Ann. Phys., 16:3 (1961), 407–466 | DOI | MR
[28] B. M. McCoy, “Spin correlation functions of the $X$–$Y$ model”, Phys. Rev., 173:2 (1968), 531–541 | DOI
[29] Th. Niemeijer, “Some exact calculations on a chain of spins 1/2”, Physica, 36:3 (1967), 377–419 | DOI
[30] S. Katsura, T. Horiguchi, M. Suzuki, “Dynamical properties of the isotropic $XY$ model”, Physica, 46:1 (1970), 67–86 | DOI
[31] J. H. H. Perk, H. W. Capel, “Time-dependent $xx$-correlation functions in the one dimensional $XY$-model”, Phys. A, 89:2 (1977), 265–303 | DOI
[32] H. G. Vaidya, C. A. Tracy, “Crossover scaling function for the one-dimensional $XY$ model at zero temperature”, Phys. Lett. A, 68:3–4 (1978), 378–380 | DOI | MR
[33] T. Tonegawa, “Transverse spin correlation function of the one-dimensional spin-$1/2$ $XY$ model”, Solid State Comm., 40:11 (1981), 983–986 | DOI
[34] M. D'lorio, U. Glaus, E. Stoll, “Transverse spin dynamics of a one-dimensional $XY$ system: A fit to spin-spin relaxation data”, Solid State Commun., 47:5 (1983), 313–315 | DOI
[35] A. G. Izergin, N. A. Kitanin, N. A. Slavnov, “O korrelyatsionnykh funktsiyakh $XY$-modeli”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 13, Zap. nauchn. sem. POMI, 224, POMI, SPb., 1995, 178–191 | DOI | MR | Zbl
[36] K. Fabricius, B. M. McCoy, “New developments in the eight vertex model”, J. Stat. Phys., 111:1–2 (2003), 323–337, arXiv: ; “New developments in the eight vertex model II. Chains of odd length”, 120:1–2 (2005), 37–70, arXiv: ; “Functional equations and fusion matrices for the eight-vertex model”, Publ. Res. Inst. Math. Sci., 40:3 (2004), 905–932, arXiv: cond-mat/0207177cond-mat/0410113cond-mat/0311122 | DOI | MR | DOI | MR | DOI | MR
[37] K. Fabricius, B. M. McCoy, “An elliptic current operator for the 8 vertex model”, J. Phys. A: Math. Gen., 39:48 (2006), 14869–14886, arXiv: cond-mat/0606190 | DOI | MR
[38] T. Deguchi, “The 8V CSOS model and the $sl_2$ loop algebra symmetry of the six-vertex model at roots of unity”, Internat. J. Modern Phys. B, 16:14–15 (2002), 1899–1905, arXiv: cond-mat/0110121 | DOI | MR
[39] K. Fabricius, “A new $Q$-matrix in the eight vertex model”, J. Phys. A: Math. Theor., 40:15 (2007), 4075–4086, arXiv: cond-mat/0610481 | DOI | MR
[40] S. Kharchev, A. Zabrodin, “Theta vocabulary I”, J. Geom. Phys., 94 (2015), 19–31, arXiv: 1502.04603 | DOI | MR