The nested Bethe ansatz for 'all' open spin chains with diagonal boundary conditions

Journal of Physics A: Mathematical and Theoretical

Volumn 42, Issue 20, 2009, Pages

  Belliard, S ^a   Ragoucy, E ^a  

^a UNIVERSITÉ DE SAVOIE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 67650898243     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/42/20/205203     Document Type: Article

References (50)

1. Cherednik I 1984 Factorizing particles on the half-line and roots systems Teor. Mat. Fiz. 61 55
2. Sklyanin E K 1988 Boundary conditions for integrable quantum systems J. Phys. A: Math. Gen. 21 2375
3. Faddeev L 1998 How algebraic Bethe ansatz works for integrable model in Symétries quantiques Les Houches Summer School Proceedings vol 64 ed A Connes, K Gawedzki and J Zinn-Justin (Amsterdam: North-Holland) (arXiv:hep-th/9605187)
4. Takhtajan L A and Faddeev L D 1979 The quantum method of the inverse problem and the Heisenberg XYZ model Russ. Math. Surv. 34 11-68
5. Kulish P P and Sklyanin E K 1979 Quantum inverse scattering method and the Heisenberg ferromagnet Phys. Lett. A 70 461-3
6. Kulish P P and Sklyanin E K 1982 Solution of the Yang-Baxter equation J. Sov. Math. 19 1596-620
7. Kulish P P and Yu Reshetikhin N 1983 Diagonalisation of invariant transfer matrices and quantum N-wave system (Lee model) J. Phys. A: Math. Gen. 16 L591-6
8. Baseilhac P and Koizumi K 2007 Exact spectrum of the XXZ open spin chain from the q-onsager algebra representation theory J. Stat. Mech. P09006 (arXiv:hep-th/0703106)
9. Baseilhac P 2007 New results in the XXZ open spin chain Proc. RAQIS07 (Annecy-le-Vieux, France) (arXiv: 0712.0452)
10. Kuniba A, Sakai K and Suzuki J 1998 Continued fraction TBA and functional relations in XXZ model at root of unity Nucl. Phys. B 525 597 (arXiv:math/9803056)
11. Nepomechie R 2002 Solving the open XXZ spin chain with nondiagonal boundary terms at roots of unity Nucl. Phys. B 622 615 (arXiv:hep-th/0110116)
12. Nepomechie R 2004 Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms J. Phys. A: Math. Gen. 37 433 (arXiv:hep-th/0304092)
13. Murgan R, Nepomechie R and Shi Chi 2006 Exact solution of the open XXZ chain with general integrable boundary terms at roots of unity J. Stat. Mech. P08006 (arXiv:hep-th/0605223)
14. Frappat L, Nepomechie R and Ragoucy E 2007 Complete Bethe Ansatz solution of the open spin-s XXZ chain with general integrable boundary terms J. Stat. Mech. P09008 (arXiv:0707.0653)
15. Cao Junpeng, Lin H-Q, Shi K-j and Wang Y 2003 Exact solutions and elementary excitations in the XXZ spin chain with unparallel boundary fields Nucl. Phys. B 663 487 (arXiv:cond-mat/0212163)
16. Galleas W and Martins M J 2005 Solution of the vertex model with non-diagonal open boundaries Phys. Lett. A 335 167 (arXiv:nlin.SI/0407027)
17. Yang W L and Zhang Y Z 2005 Exact solution of the trigonometric vertex model with non-diagonal open boundaries J. High Energy Phys. JHEP01(2005)021 (arXiv:hep-th/0411190)
18. Yu Reshetikhin N 1987 The spectrum of the transfer matrices connected with Kac-Moody algebras Lett. Math. Phys. 14 235
19. Arnaudon D, Crampé N, Doikou A, Frappat L and Ragoucy I 2005 Analytical Bethe Ansatz for closed and open -spin chains in any representation J. Stat. Mech. P02007 (arXiv:math-ph/0411021)
20. Arnaudon D, Crampé N, Doikou A, Frappat L and Ragoucy I 2006 Spectrum and Bethe ansatz equations for the closed and open spin chains in any representation Ann. H. Poincaré 7 1217 (arXiv: math-ph/0512037)
21. Ragoucy I and Satta G 2007 Analytical Bethe ansatz for closed and open super-spin chains in arbitrary representations J. High Energy Phys. JHEP09(2007)001 (arXiv:hep-th/0706.3327)
22. Belliard S and Ragoucy I 2008 The nested Bethe ansatz for 'all' closed spin chains J. Phys. A: Math. Theor. 41 295202 (arXiv:0804.2822 [math-ph])
23. n-1 vertex models J. Phys. A: Math. Gen. 26 L519 (arXiv:hep-th/9211114)
24. q(n) invariant quantum spin chains Nucl. Phys. B 417 553 (arXiv:hep-th/9309022)
25. de Vega H J and González-Ruiz A 1994 Exact Bethe ansatz solution of chains with non- invariant open boundary conditions arXiv:hep-th/9404141
26. Yue R H, Fan H and Hou B 1996 Exact diagonalisation of the quantum supersymmetric model Nucl. Phys. B 462 167 (arXiv:cond-mat/9603022)
27. Yu Reshetikhin N, Takhtajan L A and Faddeev L D 1990 Quantization of Lie Groups and Lie algebras Leningr. Math. J. 1 193-225
28. Drinfeld V G 1987 Quantum groups Proc. Int. Congress Math. (Berkeley, 1986) (Providence, RI: AMS) pp 798-820
29. Drinfeld V G 1988 A new realization of Yangians and quantized affine algebras Sov. Math. Dokl. 36 212-6
30. Jimbo M 1985 A q difference analog of U(G) and the Yang-Baxter equation Lett. Math. Phys. 10 63
31. Jimbo M 1986 A q-difference analogue of U(gl(n + 1)), Hecke algebra and the Yang-Baxter equation Lett. Math. Phys. 11 247
32. Reshetikhin N and Semenov-Tian-Shansky M 1990 Central extensions of quantum current groups Lett. Math. Phys. 19 133
33. Arnaudon D, Avan J, Crampé N, Doikou A, Frappat L and Ragoucy I 2004 General boundary conditions for the and open spin chains J. Stat. Mech. P08005 (arXiv:math-ph/0406021)
34. n boundary Yang-Baxter equation arXiv: hep-th/9911178
35. Molev A and Ragoucy I 2002 Representations of reflection algebras Rev. Math. Phys. 14 317 (arXiv: math-QA/0406021)
36. Chari V and Pressley A 1990 Yangians and R-matrices L'Enseignement Math. 36 267
37. Chari V and Pressley A 1994 A Guide to Quantum Groups (Cambridge: Cambridge University Press)
38. Molev A I 2002 Irreducibility criterion for tensor products of Yangian evaluation modules Duke Math. J. 112 307 (arXiv:math.QA/0009183)
39. Zhang R B 1996 The super-Yangian and its finite dimensional representations Lett. Math. Phys. 37 419 (arXiv:q-alg/9507029)
40. Zhang R B 1993 Finite dimensional irreducible representations of the supergroup J. Math. Phys. 34 1236
41. Rosso M 1988 Finite dimensional representations of the quantum analogue of the enveloping algebra of a complex simple Lie algebra Commun. Math. Phys. 117 581
42. Molev A I 2003 Yangians and their applications Handbook of Algebra vol 3 ed M Hazewinkel (Amsterdam: Elsevier) p 907 (arXiv:math.QA/021128)
43. Nazarov M 1991 Quantum Berezinian and the classical Capelli identity Lett. Math. Phys. 21 123
44. Belliard S and Ragoucy I Berezinian for in preparation
45. Sklyanin E, Takhtajan L and Faddeev L 1979 The quantum inverse problem method Theor. Math. Phys. 40 688
46. Mukhin E, Tarasov V and Varchenko A 2006 Bethe eigenvectors of higher transfer matrices J. Stat. Mech. P08002 (arXiv:math.QA/0605015)
47. Tarasov V and Varchenko A 2007 Combinatorial formulae for nested Bethe vector arXiv:math.QA/0702277
48. Tarasov V and Varchenko A 1994 Solutions to the quantized Knizhnik-Zamolodchikov equation and the Bethe ansatz arXiv:hep-th/9411181
49. Khoroshkin S and Pakuliak S 2005 Weight function for Theor. Math. Phys. 145 1373
50. Khoroshkin S and Pakuliak S 2007 A computation of an universal weight function for the quantum affine algebra arXiv:0711.2819 [math.QA]