Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2011-01-05
J. Math. Phys. 52:022306,2011
Physics
High Energy Physics
High Energy Physics - Lattice
LaTex, 20 pages, 5 figures
Scientific paper
10.1063/1.3546030
Borrowing ideas from tight binding model, we propose a board class of Lattice QFT models that are classified by the ADE Lie algebras. In the case of su(N) series, we show that the couplings between the quantum states living at the first nearest neighbor sites of the lattice $\mathcal{L}_{su(N)}$ are governed by the complex fundamental representations \underline{${{\mathbf{N}}}$} and $\bar{{\mathbf{N}}}$ of $su(N)$; and the second nearest neighbor interactions are described by its adjoint $\underline{\mathbf{N}} \otimes \bar{\mathbf{N}}$. The lattice models associated with the leading su(2), su(3) and su(4) cases are explicitly studied and their fermionic field realizations are given. It is also shown that the su(2) and su(3) models describe respectively the electronic properties of the acetylene chain and the graphene. It is established as well that the energy dispersion of the first nearest neighbor couplings is completely determined by the $A_{N}$ roots $ \mathbf{\alpha}$ through the typical dependence $N/2+\sum_{roots}\cos(\mathbf{k}.\alpha) $ with $\mathbf{k}$ the wave vector. Other features such as DE extension and other applications are also discussed. Keywords: Tight Binding Model, Graphene, Lattice QFT, ADE Symmetries.
Bousmina Mosto
Drissi Lalla Btissam
Saidi El Hassan
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