Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics A Mathematical and General

Temperley-Lieb lattice models arising from quantum groups

Murray T. Batchelor, A Kuniba

Published Feb 21, 1992• 4 citations
Publisher
DOI
10.1088/0305-4470/25/4/036

Related papers

Topological Defects in Lattice Models and Affine Temperley–Lieb Algebra

Jonathan Belletête, Azat M. Gainutdinov, Jesper Lykke Jacobsen +2 more

arXiv:1811.02551•Communications in Mathematical Physics•Mar 7, 2023•20 citations

Temperley-Lieb-Jones algebra approach to Heisenberg spin models

Yan Hong, Shao-Ming Fei

•Jan 1, 1993•0 citations

Quantum Groups in Lattice Models

Vincent Pasquier

NATO ASI series. Series B : Physics•Jan 1, 1992•1 citation

Temperley-Lieb lattice models arising from quantum groups

Murray T. Batchelor, Atsuo Kuniba

The authors construct families of solvable quantum spin chains, vertex and interactions round a face (IRF) models from representations of the Temperley-Lieb algebra associated with the quantum groups U q (X n ) for X n =A 1 , B n , C n and D n . They determine a correlation measuring order in the IRF models via the fusion rule in the level l X n (1) . Wess-Zumino-Witten model.

Journal of Physics A Mathematical and General•Jun 7, 1991•39 citations

The Temperley-Lieb-Jones Algebra and Symmetry Group in Heisenberg Spin Models in One and Two Dimensions

Shao-Ming Fei, Hong Yan

We present a systematic method to construct the spin models of Heisenberg type in higher dimensions with nearest and non-nearest neighbour interactions. These models constructed in this way are of Temperley-Lieb-Jones (TLJ) algebraic structures and -invariances. The TLJ algebra is generalized to adjusting the lattice spin models. The Hamiltonians of Heisenberg spin models in one dimension (including second nearest neighbour interactions) and in two-dimensional triangular lattice (with nearest interaction) are constructed explicitly. The hidden symmetries are shown to be the group, and the terms in Hamiltonian for different lattice cells are explicitly shown to be the representations of elements of (TLJ) algebra.

Communications in Theoretical Physics•Jan 1, 1993•1 citation

Classical integrable lattice models through quantum group related formalism

A. Kundu

arXiv:hep-th/9402101•Theoretical and Mathematical Physics•Jun 1, 1994•1 citation
We present a systematic method to construct the spin models of Heisenberg type in higher dimensions with nearest and non-nearest neighbour interactions. These models constructed in this way are of Temperley-Lieb-Jones (TLJ) algebraic structures and -invariances. The TLJ algebra is generalized to adjusting the lattice spin models. The Hamiltonians of Heisenberg spin models in one dimension (including second nearest neighbour interactions) and in two-dimensional triangular lattice (with nearest interaction) are constructed explicitly. The hidden symmetries are shown to be the group, and the terms in Hamiltonian for different lattice cells are explicitly shown to be the representations of elements of (TLJ) algebra.