Geodesic
Algebraic Bethe ansatz for seven-vertex model
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 20, Tome 347 (2007), pp. 178-186 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The work is dedicated to the construction of algebraic Bethe ansatz for seven-vertex model. $R$-matrix of the system is obtained by means of twist from six-vertex model consider by us earlier. The presence of seven nonzero element in $R$-matrix complicates the situation. In particular the commutation relations of elements of monodromy matrix becomes more difficult in comparison with the six-vertex model. But we construct algebraic Bethe ansatz by help of introducing of new operator that is the difference between two operators on the main diagonal of monodromy matrix. The eigenstates and the spectrum of the system were found. This is the first step on the way of comparison of the systems with six- and seven-vertex $R$-matrix respectively. 
@article{ZNSL_2007_347_a10,
     author = {P. P. Kulish and P. D. Ryasichenko},
     title = {Algebraic {Bethe} ansatz for seven-vertex model},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {178--186},
     year = {2007},
     volume = {347},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_347_a10/}
}
TY  - JOUR
AU  - P. P. Kulish
AU  - P. D. Ryasichenko
TI  - Algebraic Bethe ansatz for seven-vertex model
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2007
SP  - 178
EP  - 186
VL  - 347
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2007_347_a10/
LA  - ru
ID  - ZNSL_2007_347_a10
ER  - 
%0 Journal Article
%A P. P. Kulish
%A P. D. Ryasichenko
%T Algebraic Bethe ansatz for seven-vertex model
%J Zapiski Nauchnykh Seminarov POMI
%D 2007
%P 178-186
%V 347
%U http://geodesic.mathdoc.fr/item/ZNSL_2007_347_a10/
%G ru
%F ZNSL_2007_347_a10
P. P. Kulish; P. D. Ryasichenko. Algebraic Bethe ansatz for seven-vertex model. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 20, Tome 347 (2007), pp. 178-186. http://geodesic.mathdoc.fr/item/ZNSL_2007_347_a10/

[1] L. D. Faddeev, “How algebraic Bethe Ansatz works for integrable model”, Quantum Symmetries /Symmetries Quantiques, eds. A. Connes et al., North-Holland, Amsterdam, 1998, 149–219 | 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 transformed method. Recent developments”, Lect. Notes Phys., 151, 1982, 61–159 | MR

[4] P. P. Kulish, P. D. Ryasichenko, “Spinovaya tsepochka, svyazannaya s kvantovoi superalgebroi $sl_q(1/1)$”, Zap. nauchn. semin. POMI, 325, 2005, 146–162 | MR | Zbl

[5] V. Korepin, Comm. Math. Phys., 86 (1982), 391–418 | DOI | MR | Zbl

[6] E. V. Damaskinskii, P. P. Kulish, “Simmetrii, svyazannye s uravneniem Yanga–Bakstera i uravneniem otrazheniya”, Zap. nauchn. semin. POMI, 269, 2000, 180–192 | MR | Zbl

[7] F. C. Alcaraz, M. Droz, M. Henkel and V. Rittenberg, “Reactin-diffusion processes, critical dynamics, and quantum chains”, Ann. Phys., 230 (1994), 250–302 | DOI | MR | Zbl

[8] H. Hinrichsen and V. Rittenberg, “A two-parameter deformation of the $su(1,1)$ superalgebra and $XY$ quantum spin chain in a magnetic field”, Phys. Lett. B, 275 (1992), 350–354 | DOI | MR