Two types of boundary conditions ("soliton preserving" and "soliton non-preserving") are investigated for the sl(n) and sl(m|n) open spin chains. The appropriate reflection equations are formulated and the corresponding solutions are classified. The symmetry and the Bethe Ansatz equations are derived for each case. The general treatment for non-diagonal reflection matrices associated to "soliton preserving" case is worked out. The connection between the "soliton non-preserving" boundary conditions and the twisted (super) Yangians is also discussed.
Publié le : 2004-07-05
Classification:
Yangiens,
Chaînes de spins,
conditions de bord,
équations de réflexion,
Ansatz de Bethe analytique,
MSC: 81R50, 17B37 ; PACS: 02.20.Uw, 03.65.Fd, 75.10.Pq,
[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th],
[PHYS.COND.CM-SCE]Physics [physics]/Condensed Matter [cond-mat]/Strongly Correlated Electrons [cond-mat.str-el],
[MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA]
@article{hal-00001684,
author = {Arnaudon, Daniel and Avan, Jean and Cramp\'e, Nicolas and Doikou, Anastasia and Frappat, Luc and Ragoucy, Eric},
title = {General boundary conditions for the sl(N) and sl(M|N) open spin chains},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00001684}
}
Arnaudon, Daniel; Avan, Jean; Crampé, Nicolas; Doikou, Anastasia; Frappat, Luc; Ragoucy, Eric. General boundary conditions for the sl(N) and sl(M|N) open spin chains. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00001684/