Temperley-Lieb Words as Valence-Bond Ground States

TL;DR

This paper introduces a class of one-dimensional Hamiltonians derived from the Temperley-Lieb algebra, with ground states represented as algebraic words, generalizing known models and enabling correlation function calculations.

Contribution

It defines new Hamiltonians based on the Temperley-Lieb algebra and constructs their ground states as algebraic words, extending the Majumdar-Ghosh model to a broader algebraic framework.

Findings

Ground states expressed as words of the algebra

Two-point correlation functions computed using Temperley-Lieb relations

Generalization of the Majumdar-Ghosh model with 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.