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Ab initio Many-Body Perturbation Theory in Condensed Matter: From conventional numerical approaches to Machine Learning
Paolo Emilio Trevisanutto
Excitons, electron-hole (e-h) quasi-particle and plasmons have important roles in fundamental and applied physics, especially for 2D materials where the binding energy is high: stable and localized excitons that can be exploited either for qubits or, by using the self-trapping effects, for Single Light Emitter devices, whereas plasmons are involved, for instance, in the Polariton, Solar Cell and Organic Light-Emitting Devices. In this talk, we review the current state of the art from the ab initio many-body perturbation theory (MBPT), the GW-Bethe-Salpeter Equation (GW-BSE) in the linear regime. In addition, we report a theoretical approach (the Time-dependent Bethe-Salpeter Equation(TD-BSE)) in order to study the nonlinear optical response. In parallel, we present a Statistical Mechanics (SM) model of deep neural networks, connecting the energy-based and feedforward networks (FFN) approach. We infer that FFN can be understood as performing three basic steps: encoding, representation validation and propagation. Finally, we will discuss the possibility of inserting deep neural network approaches to improve and expedite the ab initio MBPT calculations in Condensed Matter Physics.