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The Temperley-Lieb-Jones Algebra and Symmetry Group in Heisenberg Spin Models in One and Two Dimensions
Authors:Shao-Ming FEI  Hong YAN
Institution:1. CCAST (World Laboratory), P.O. Box 8730, Beijing 100080, China; 2. Institute of Theoretical Physics, Academia Sinica, P.O. Box 2735, Beijing 100080, China
Abstract:We present a systematic method to construct the spin models of Heisenberg type in higher dimensions with nearesband non-nearest neighbour interactions. These models constructed in this way are of Temperley-Lieb-Jones (TLJ) algebraic structures and SU(2)-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 SU(2) group, and the terms in Ilamiltonian for different lattice cells are explicitly shown to be the representations of elements of (TLJ) algebra.
Keywords:
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