Dimer representations of the Temperley-Lieb algebra
classification
🧮 math-ph
cond-mat.stat-mechhep-thmath.MP
keywords
dimeralgebradimensionrepresentationrepresentationsspin-chaintemperley-liebanalysis
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A new spin-chain representation of the Temperley-Lieb algebra $TL_n(\beta=0)$ is introduced and related to the dimer model. Unlike the usual XXZ spin-chain representations of dimension $2^n$, this dimer representation is of dimension $2^{n-1}$. A detailed analysis of its structure is presented and found to yield indecomposable zigzag modules.
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