Journal article

Bethe ansatz for the Temperley-Lieb loop model with open boundaries - art. no P002

J de Gier, P Pyatov

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT | IOP PUBLISHING LTD | Published : 2004

Abstract

We diagonalize the Hamiltonian of the Temperley-Lieb loop model with open boundaries using a coordinate Bethe ansatz calculation. We find that in the ground-state sector of the loop Hamiltonian, but not in other sectors, a certain constraint on the parameters has to be satisfied. This constraint has a natural interpretation in the Temperley-Lieb algebra with boundary generators. The spectrum of the loop model contains that of the quantum spin-1/2 XXZ chain with non-diagonal boundary conditions. We hence derive a recently conjectured solution of the complete spectrum of this XXZ chain. We furthermore point out a connection with recent results for the two-boundary sine-Gordon model. © IOP Publ..

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