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arXiv · hep-th/0312235

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

Jan de Gier·Pavel Pyatov
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Abstract

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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Jan de Gier, Pavel Pyatov. 2004-02-26. Bethe Ansatz for the Temperley-Lieb loop model with open boundaries. https://doi.org/10.1088/1742-5468%2F2004%2F03%2Fp002

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