One-boundary Temperley-Lieb algebras in the XXZ and loop models

Abstract

We give an exact spectral equivalence between the quantum group invariant XXZ chain with arbitrary left boundary term and the same XXZ chain with purely diagonal boundary terms. This equivalence, and a further one with a, link pattern Hamiltonian, can be understood as arising from different representations of the one-boundary Temperley-Lieb algebra. For a system of size L these representations are all of dimension 2 and, for generic points of the algebra, equivalent. However, at exceptional points they can possess different indecomposable structures. We study a centralizer of the one-boundary Temperley-Lieb algebra in the 'non-diagonal' spin-1/2 representation and find its eigenvalues and e..