An SU(3) Yang-Mills Structure for Electron-Phonon Interactions Resulting from Strong Electron Correlations in 2D hexagonal lattices

Concise and powerful mathematical descriptions of the interplay of spin and charge degrees of degrees of freedom with crystal lattice fluctuations are of extreme importance in materials science. Such descriptions allow structured approaches to optimizing material efficiencies resulting in considerable resource savings and higher performance devices. In this work, by re-imagining the the Gell-Mann matrices as 3$\times$3 linear transformations acting on a column vector of position states, an SU(3) theory of the interplay between lattice fluctuations and strong electron correlations in 2-dimensional hexagonal materials such as graphene is formulated.