Bethe Ansatz for the Temperley-Lieb loop model with open boundaries

Details Bethe Ansatz for the Temperley-Lieb loop model with open boundaries Bethe Ansatz for the Temperley-Lieb loop model with open boundaries

2003-12-19

arxiv.org/abs/hep-th/0312235v2

J.Stat.Mech.0403:P03002,2004

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 31 pages, 14 EPS figures, minor corrections

Scientific paper

10.1088/1742-5468/2004/03/P002

We diagonalise the Hamiltonian of the Temperley-Lieb loop model with open boundaries using a coordinate Bethe Ansatz calculation. We find that in the groundstate 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.

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