Characterization 1-D Hubbard systems with long-range Coulomb interaction using machine learning: effect of disorder and system size

One-dimensional atomic chains with long-range Coulomb interactions are ideal models for studying many-body behavior. Quantized plasmonic excitations can be identified in chains as short as 8 atoms and can be launched and transferred across the chain by coupling to quantum emitters. By varying the amount of disorder in both the strength of the hopping between nearest neighbor sites and the electron-electron Coulomb interaction, we observe the localization landscape of the plasmon. We characterize the effects of disorder using a combination of exact diagonalization and machine learning algorithms and establish relations between distortion of the quantization and specific types of disorder using parameters such as the inverse participation ratio. We establish different regimes of disorder where phenomena such as Many Body Localization will onset. Additionally, we will discuss the application of Matrix Product State (MPS) algorithms on larger systems, which are infeasible for exact diagonalization, to understand quantization, disorder and localization in larger systems.