On reflection algebras and twisted Yangians

Journal Article · Sun May 01 04:00:00 EDT 2005 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.1888029· OSTI ID:20699180

Doikou, Anastasia ^[1]

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1. Laboratoire d'Annecy-le-Vieux de Physique Theorique, LAPTH, CNRS, UMR 5108, Universite de Savoie, B.P. 110, F-74941 Annecy-le-Vieux Cedex (France)

It is well known that integrable models associated to rational R matrices give rise to certain non-Abelian symmetries known as Yangians. Analogously boundary symmetries arise when general but still integrable boundary conditions are implemented, as originally argued by Delius, Mackay, and Short from the field theory point of view, in the context of the principal chiral model on the half-line. In the present study we deal with a discrete quantum mechanical system with boundaries, that is the N site gl(n) open quantum spin chain. In particular, the open spin chain with two distinct types of boundary condition known as soliton preserving and soliton nonpreserving is considered. For both types of boundaries we present a unified framework for deriving the corresponding boundary nonlocal charges directly at the quantum level. The nonlocal charges are simply coproduct realizations of particular boundary quantum algebras called boundary or twisted Yangians, depending on the choice of boundary conditions. Finally, with the help of linear intertwining relations between the solutions of the reflection equation and the generators of the boundary or twisted Yangians we are able to exhibit the exact symmetry of the open spin chain, namely we show that a number of the boundary nonlocal charges are in fact conserved quantities.

• OSTI ID: 20699180
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 5 Vol. 46; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
BOUNDARY CONDITIONS
BOUNDARY-VALUE PROBLEMS
CHIRALITY
EQUATIONS
FIELD THEORIES
INTEGRAL CALCULUS
MATHEMATICAL SOLUTIONS
QUANTUM MECHANICS
R MATRIX
REFLECTION
SOLITONS
SPIN
SYMMETRY