Simulating plasmonic behaviors in large fermionic arrays

It is known that interesting plasmonic behavior can arise from small fermionic systems with Coulomb interactions. With techniques such as the Density Matrix Renormalization Group (DMRG), we explored the possibility of simulating 1-D fermionic systems with dimensions well beyond the limits of Exact Diagonalization (ED), and observing plasmonic behaviors, such as the asymptotically perfect quantization of plasmonic excitations, on scales that were previously numerically infeasible. With possible imperfect lattice realization in experiments in mind, we also studied the effects of disorder on these system, through combination of machine learning techniques and data from both ED and advanced tensor network algorithms. We observed the power of Convolutional Neural Network (CNN) in learning about the distribution of various localization metrics, as well as important many-body physical quantities such as the Generalized Plasmonicity Index. We concluded by comments on our current efforts in simulating larger 2-D fermionic systems as well as open systems.