General boundary conditions for the sl(N) and sl(M|N) open spin chains

Daniel Arnaudon (1) , Jean Avan (2) , Nicolas Crampé (1) , Anastasia Doikou (1) , Luc Frappat (1) , Eric Ragoucy (1)

1 LAPTH - Laboratoire d'Annecy-le-Vieux de Physique Théorique
2 LPTM - UMR 8089 - Laboratoire de Physique Théorique et Modélisation

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.

Mots clés: Yangiens; Chaînes de spins; conditions de bord; équations de réflexion; Ansatz de Bethe analytique

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Electrons fortement corrélés [cond-mat.str-el]; Algèbres quantiques [math.QA]

Daniel Arnaudon, Jean Avan, Nicolas Crampé, Anastasia Doikou, Luc Frappat, et al.. General boundary conditions for the sl(N) and sl(M|N) open spin chains. Journal of Statistical Mechanics: Theory and Experiment, 2004, 08, pp.P005. ⟨10.1088/1742-5468/2004/08/P08005⟩. ⟨hal-00001684v3⟩