Costa, Emanuele (2024) Deep learning density functional theory for simulating quantum many-body systems. [Tesi di dottorato]

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In recent years, a generalization of density functional theory for the purpose of simulating quantum many-body systems has been developed. Moreover, the development of Deep Learning techniques improved in both accuracy and speed up the application of Density Functional Theory in electronic structure and material science. his thesis introduces a novel method employing DL-density functionals for simulating quantum many-body systems. We delve into the deep learning orbital-free method, exploring its limitations within the electronic structure framework. Our approach involves introducing a new architecture and employing an adaptive manifold restriction via Variational Autoencoder to fix the gradient instability during optimization. Extending DFT to spin Hamiltonians, we examine the conditions ensuring its suitability in spin systems and integrate DL-DFT techniques into this framework. Using scalable neural networks, we predict ground state properties in larger system sizes, uncovering insights into scalability and Quantum Phase transitions. Furthermore, we study the generalization of DL-DFT for simulating the dynamics of spin Hamiltonians. We generalize the Kohn-Sham equations for spin systems and we use the adiabatic approximation to study the dynamics by using DL-DFT functionals. Finally, we demonstrate a practical application of Deep Learning in physics: using D-Wave datasets to simulate the thermodynamics of a spin glass, showcasing DL's potential in this field.

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