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Temperley-Lieb Words as Valence-Bond Ground States

Peter F Arndt·Thomas Heinzel·C M Yung
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Abstract

Based on the Temperley--Lieb algebra we define a class of one-dimensional Hamiltonians with nearest and next-nearest neighbour interactions. Using the regular representation we give ground states of this model as words of the algebra. Two point correlation functions can be computed employing the Temperley--Lieb relations. Choosing a spin-1/2 representation of the algebra we obtain a generalization of the (q-deformed) Majumdar--Ghosh model. The ground states become valence-bond states.

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Peter F Arndt, Thomas Heinzel, C M Yung. 1994-11-21. Temperley-Lieb Words as Valence-Bond Ground States. https://doi.org/10.1088/0305-4470%2F28%2F12%2F001

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