English

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

High Energy Physics - Theory 2011-02-16 v2 Statistical Mechanics

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.

Keywords

Cite

@article{arxiv.hep-th/0312235,
  title  = {Bethe Ansatz for the Temperley-Lieb loop model with open boundaries},
  author = {Jan de Gier and Pavel Pyatov},
  journal= {arXiv preprint arXiv:hep-th/0312235},
  year   = {2011}
}

Comments

LaTeX, 31 pages, 14 EPS figures, minor corrections

R2 v1 2026-07-22T15:20:47.969Z