Dimer representations of the Temperley-Lieb algebra

Abstract

A new spin-chain representation of the Temperley-Lieb algebra $T{L}_n(\beta =0)$ 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.

arXiv comment23 pages. Comments and references added

References in corpus (9)

• Logarithmic Minimal Models
• Associative-algebraic approach to logarithmic conformal field theories
• An introduction to the dimer model
• Solvable Critical Dense Polymers
• Lattice fusion rules and logarithmic operator product expansions
• Fusion Algebras of Logarithmic Minimal Models
• Standard Modules, Induction and the Temperley-Lieb Algebra
• Refined conformal spectra in the dimer model
• Transfer matrix for spanning trees, webs and colored forests

Cited by in corpus (10)

• Integrability and conformal data of the dimer model
• Restriction and induction of indecomposable modules over the Temperley-Lieb algebras
• On the reality of spectra of ${\mathbf{U}}_{\mathbf{q}}(\mathbf{s}{\mathbf{l}}_2)$-invariant XXZ Hamiltonians
• Yang-Baxter Solution of Dimers as a Free-Fermion Six-Vertex Model
• Topological sectors, dimer correlations and monomers from the transfer-matrix solution of the dimer model
• Fusion rules for the Temperley-Lieb algebra and its dilute generalisation
• Thermodynamic properties of the macroscopically degenerate tetramer-dimer phase of the spin-1/2 Heisenberg model on the diamond-decorated square lattice
• Integrable Floquet systems related to logarithmic conformal field theory
• Yang-Baxter Integrable Dimers on a Strip
• Multipoint correlators in the Abelian sandpile model