On integrable Hamiltonians for higher spin \(XXZ\) chain. (English) Zbl 1062.82011
Summary: Integrable Hamiltonians for higher spin periodic \(XXZ\) chains are constructed in terms of the spin generators; explicit examples for spins up to \(3 \over 2\) are given. Relations between Hamiltonians for some \(U_q(sl_2)\)-symmetric and \(U(1)\)-symmetric universal \(r\)-matrices are studied; their properties are investigated. A certain modification of the higher spin periodic chain Hamiltonian is shown to be an integrable \(U_q(sl_2)\)-symmetric Hamiltonian for an open chain.
MSC:
| 82B23 | Exactly solvable models; Bethe ansatz |
| 37N20 | Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) |
| 81R12 | Groups and algebras in quantum theory and relations with integrable systems |
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
References:
| [1] | Kulish, J. Sov. Math. 23 pp 2435– (1983) |
| [2] | Sklyanin, Funct. Anal. Appl. 17 pp 273– (1983) |
| [3] | Zamolodchikov, Sov. J. Nucl. Phys. 32 pp 298– (1980) |
| [4] | Sogo, Phys. Lett. A 104 pp 51– (1984) |
| [5] | Babujian, Nucl. Phys. B 265 pp 24– (1986) |
| [6] | Kirillov, J. Phys. A 20 pp 1565– (1987) |
| [7] | Reshetikhin, J. Phys. A 20 pp 1587– (1987) |
| [8] | Alcaraz, J. Phys. A 22 pp 1829– (1989) |
| [9] | Faddeev, Theor. Math. Phys. 57 pp 1059– (1983) |
| [10] | Faddeev, Leningrad Math. J. 1 pp 193– (1990) |
| [11] | Jimbo, Lett. Math. Phys. 10 pp 63– (1985) |
| [12] | Jimbo, Commun. Math. Phys. 102 pp 537– (1986) |
| [13] | Kulish, Lett. Math. Phys. 5 pp 393– (1981) |
| [14] | L. D. Faddeev,How Algebraic Bethe Ansatz Works for Integrable Model, in Symétries Quantiques (Les Houches, 1995) (North-Holland, Amsterdam, 1998), pp. 149–219 [hep-th/9605187]. · Zbl 0934.35170 |
| [15] | Kulish, Lect. Notes Phys. 151 pp 61– (1982) |
| [16] | Faddeev, Sov. Sci. Rev., Sect. C, Math. Phys. Rev. 1 pp 107– (1980) |
| [17] | Babujian, Phys. Lett. A 90 pp 479– (1982) |
| [18] | Masuda, Lett. Math. Phys. 19 pp 187– (1990) |
| [19] | Drinfeld, Leningrad Math. J. 1 pp 1419– (1990) |
| [20] | Reshetikhin, Lett. Math. Phys. 20 pp 331– (1990) |
| [21] | Maillet, Am. Math. Soc. Trans. 201 pp 137– (1996) |
| [22] | de Santos |
| [23] | Kulish, Czech. J. Phys. 47 pp 1207– (1997) |
| [24] | Stolin |
| [25] | Foerster, J. Phys. A 31 pp 687– (1998) |
| [26] | Alcaraz, J. Phys. A 20 pp 6397– (1987) |
| [27] | Pasquier, Nucl. Phys. B 330 pp 523– (1990) |
| [28] | Sklyanin, J. Phys. A 21 pp 2375– (1988) |
| [29] | Mezincescu, Phys. Lett. A 147 pp 70– (1990) |
| [30] | Kulish, J. Phys. A 24 pp L435– (1991) |
| [31] | Frahm, J. Phys. A 32 pp 1547– (1999) |
| [32] | Links, J. Math. Phys. 40 pp 726– (1999) |
| [33] | Cherednik, Theor. Math. Phys. 61 pp 977– (1984) |
| [34] | Fring, Nucl. Phys. B 421 pp 159– (1994) |
| [35] | Ghoshal, Int. J. Mod. Phys. A 9 pp 3841– (1994) |
| [36] | Kulish, Prog. Theor. Phys. 89 pp 741– (1993) |
| [37] | Kulish, Lett. Math. Phys. 18 pp 143– (1989) |
| [38] | Saleur, Nucl. Phys. B 336 pp 363– (1990) |
| [39] | Delius, Nucl. Phys. B 432 pp 377– (1994) |
| [40] | Tarasov, Theor. Math. Phys. 63 pp 440– (1985) |
| [41] | Faddeev, Theor. Math. Phys. 92 pp 837– (1992) |
| [42] | Faddeev, Phys. Lett. B 315 pp 311– (1993) |
| [43] | Drinfeld, Leningrad Math. J. 1 pp 321– (1990) |
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