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Construction of the Temperley-Lieb algebra from bond algebra: From the transverse-field Ising to the XXZ

We show that the Temperley-Lieb algebra is constructed from the generators of the transverse-field Ising-type bond algebra. It is also shown that, when we take the representation of the generators to the one-dimensional transverse-field Ising model, then the Temperley-Lieb algebra constructed on three consecutive bond generators becomes the XXZ model. Furthermore, we obtain several integrable spin systems from other representations for the bond generators.

preprint2022arXivOpen access
Yukihisa Imamura
cond-mat.stat-mechmath-phmath.MP
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Yukihisa Imamura

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