Geodesic
Three-magnon problem and integrability of rung-dimerized spin ladders
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 21, Tome 374 (2010), pp. 44-57 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Integrability problem for rung-dimerized spin ladder is studied by coordinate Bethe Ansatz method in three-magnon sector. It is shown that solvability of the three-magnon problem takes place for the same values of coupling constants in the Hamiltonian which guaranty solvability of the Yang–Baxter equation for the corresponding $R$-matrix. Bibl. – 15 titles. 
@article{ZNSL_2010_374_a2,
     author = {P. N. Bibikov and P. P. Kulish},
     title = {Three-magnon problem and integrability of rung-dimerized spin ladders},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {44--57},
     year = {2010},
     volume = {374},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_374_a2/}
}
TY  - JOUR
AU  - P. N. Bibikov
AU  - P. P. Kulish
TI  - Three-magnon problem and integrability of rung-dimerized spin ladders
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2010
SP  - 44
EP  - 57
VL  - 374
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2010_374_a2/
LA  - ru
ID  - ZNSL_2010_374_a2
ER  - 
%0 Journal Article
%A P. N. Bibikov
%A P. P. Kulish
%T Three-magnon problem and integrability of rung-dimerized spin ladders
%J Zapiski Nauchnykh Seminarov POMI
%D 2010
%P 44-57
%V 374
%U http://geodesic.mathdoc.fr/item/ZNSL_2010_374_a2/
%G ru
%F ZNSL_2010_374_a2
P. N. Bibikov; P. P. Kulish. Three-magnon problem and integrability of rung-dimerized spin ladders. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 21, Tome 374 (2010), pp. 44-57. http://geodesic.mathdoc.fr/item/ZNSL_2010_374_a2/

[1] L. D. Faddeev, “How algebraic Bethe Ansatz works for integrable models”, Quantum symmetries/Symmetries quantique, Proceedings of the Les Houches summer school, Session LXIV, eds. A. Connes, K. Gawedzki, J. Zinn-Justin, North-Holland, 1998 | MR | Zbl

[2] N. M. Bogolyubov, A. G. Izergin, V. E. Korepin, Korrelyatsionnye funktsii integriruemykh sistem i kvantovyi metod obratnoi zadachi, Nauka, M., 1992 | MR | Zbl

[3] P. P. Kulish, E. K. Sklyanin, “Quantum spectral transform method. Recent developments”, Proc. Symp. on Integrable Quantum Fields, Lect. Notes in Physics, 151, eds. J. Hietarinta, C. Montonen, Springer, New York, 1982 | MR

[4] L. A. Takhtadzhyan, L. D. Faddeev, “Kvantovyi metod obratnoi zadachi i XYZ model Geizenberga”, UFN, 34 (1979), 13 | MR

[5] M. Goden, Volnovaya funktsiya Bete, Mir, M., 1987 | MR

[6] T. Kennedy, “Solutions of the Yang–Baxter equation for isotropic quantum spin chains”, J. Phys. A Math. Gen., 25 (1992), 2809 | DOI | MR | Zbl

[7] K.-H. Mütter, A. Schmitt, “Solvable spin-1 models in one dimension”, J. Phys. A Math. Gen., 28 (1995), 2265 | DOI | MR | Zbl

[8] P. N. Bibikov, “How to solve Yang–Baxter equation using the Taylor expansion of $R$-matrix”, Phys. Lett. A, 314 (2003), 209–213 | DOI | MR | Zbl

[9] V. Gritsev, D. Baeriswyl, “Exactly solvable isotropic spin-$\frac12$ ladder models”, J. Phys. A Math. Gen., 36 (2003), 12129–12142 | DOI | MR | Zbl

[10] P. N. Bibikov, “A three-magnon problem for exactly rung-dimerized spin ladders: from a general outlook to the Bethe ansatz”, J. Phys. A Math. Gen., 42 (2009), 315212 | DOI | MR | Zbl

[11] P. N. Bibikov, “$R$-matritsy dlya $\mathrm{SU}(2)$-invariantnykh sdvoennykh spinovykh tsepochek”, Zap. nauchn. semin. POMI, 291, 2001, 24–34 | MR | Zbl

[12] M. T. Batchelor, X.-W. Guan, N. Oelkers, Z. Tsuboi, “Integrable models and quantum spin ladders: comparison between theory and experiment for the strong coupling ladder compounds”, Adv. Phys., 56 (2007), 465–543 | DOI

[13] B. Sutherland, “Model for a multicomponent quantum system”, Phys. Rev. B, 12 (1975), 3795 | DOI

[14] Yu. G. Stroganov, “A new calculation method for partition functions in some lattice models”, Phys. Lett. A, 74 (1979), 116–118 | DOI | MR

[15] A. G. Bytsko, “Ob odnom anzatse dlya $\mathrm{sl}_2$-invariantnykh $R$-matrits”, Zap. nauchn. semin. POMI, 335, 2006, 100–118 | MR | Zbl