Temperley-Lieb Words as Valence-Bond Ground States

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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References in corpus (2)

• Matrix-product-groundstates for one-dimensional spin-1 quantum antiferromagnets
• On the Two-Point Correlation Function for the $U_q[SU(2)]$ Invariant Spin One-Half Heisenberg Chain at Roots of Unity

Cited by in corpus (2)

• Phase Diagram of the Heisenberg Spin Ladder with Ring Exchange
• Exactly soluble isotropic spin-1/2 ladder models