Eigenvectors of open XXZ and ASEP models for a class of non-diagonal boundary conditions

Nicolas Crampé (1) , Eric Ragoucy (2) , Damien Simon (3)

1 LPTA - Laboratoire de Physique Théorique et Astroparticules
2 LAPTH - Laboratoire d'Annecy-le-Vieux de Physique Théorique
3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We present a generalization of the coordinate Bethe ansatz that allows us to solve integrable open XXZ and ASEP models with non-diagonal boundary matrices, provided their parameters obey some relations. These relations extend the ones already known in the literature in the context of algebraic or functional Bethe ansatz. The eigenvectors are represented as sums over cosets of the BC(n) Weyl group.

Mots clés: quantum integrability (Bethe ansatz); rigorous results in statistical mechanics; BETHE-ANSATZ SOLUTION; ASYMMETRIC EXCLUSION PROCESS; QUANTUM-ALGEBRA SYMMETRY; OPEN SPIN CHAINS; FUNCTIONAL RELATIONS; QUADRATIC ALGEBRA; TERMS; REPRESENTATIONS; EQUATIONS; FIELDS; quantum integrability (Bethe ansatz)

Domaines: Mécanique statistique [cond-mat.stat-mech]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Nicolas Crampé, Eric Ragoucy, Damien Simon. Eigenvectors of open XXZ and ASEP models for a class of non-diagonal boundary conditions. Journal of Statistical Mechanics: Theory and Experiment, 2010, Issue November 2010, pp.P11038. ⟨10.1088/1742-5468/2010/11/P11038⟩. ⟨hal-00520424⟩