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