Regensburg 2025 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 17: Correlated Electrons: Method Development
TT 17.14: Vortrag
Dienstag, 18. März 2025, 13:00–13:15, H33
Mapping energy functionals and external potential of V- representable charge densities of interacting quantum systems — •Calin-Andrei Pantis-Simut1, 2, Amanda Teodora Preda1, 2, and George Alexandru Nemnes1, 2 — 1Horia Hulubei National Institute for Physics and Nuclear Engineering, Reactorului 30, 077125 Magurele-Ilfov, Romania — 2Faculty of Physics, University of Bucharest, Atomistilor 405, 077125 Magurele-Ilfov, Romania
Quantum systems are shaping the modern information processing technologies. Designing and analyzing these systems yields one of the most outstanding challenges in modern physics. These systems are fairly complex due to the Coulomb interaction between the particles. There are several methods for solving these problems, the most accurate providing solutions beyond mean-field approaches. Here the Exact Diagonalization is regarded as the gold standard for a system containing several particles. Recently, charge densities of such systems have been successfully mapped from randomly generated external potentials, using cGANs models. In this work, we intend to develop a machine learning based-model in order to obtain energy functionals E[n] for several classes of Hamiltonians (e.g. containing spin-orbit interaction), thus enabling the bypass of numerical intensive procedures like Exact Diagonalization. For this task, we employ CNNs to map the energy functionals from the ground state charge density. A more in depth analysis of the inverse problem is employed also in this work. Successfully mapping the external potential is not trivial since not every proposed charge density is V-representable.
Keywords: Machine Learning; Quantum systems; Exact Diagonalization; Inverse problem; Energy functionals