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CARRASCO ARANGO MIGUEL.pdf (25.4 MB)

Tipus de document

Treball de fi de màster

Data de publicació

2025-09

Llicència de publicació

cc-by-nc-nd (c) Carrasco, 2025
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/223230

Neural Quantum States: Fermions on D-Dimensions

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Resum

In this work, we explore the use of Neural Quantum States to approximate the ground-state wavefunctions of fully polarized fermionic systems confined in a D-dimensional harmonic trap. Building on the architecture introduced in [1], we generalize the input representation and network structure to handle arbitrary spatial dimensionality, extending the applicability of the method beyond one-dimensional systems. The antisymmetric nature of the fermionic wavefunction is preserved through the use of equivariant neural layers, and a generalized Slater determinant is constructed from learned single-particle orbitals modulated by a Gaussian envelope. Training is carried out in two stages: first, a supervised pretraining phase based on analytical solutions of the non-interacting system, which is then followed by variational Monte Carlo optimization of the network parameters using the energy as the loss function. We validate our approach on non-interacting systems with up to 4 particles in 2D and 3 particles in 3D, where analytical solutions are available for benchmarking. Results show excellent agreement in terms of mean energy, one-body density, and the one-body density matrix, with observed spatial symmetries and degeneracy patterns matching theoretical expectations. While the training protocol has been generalized to incorporate finite-range interactions, this study focuses on non-interacting systems to establish a solid baseline. The framework developed here provides a flexible and scalable foundation for future exploration of interacting quantum systems in higher dimensions using neural variational methods.

Descripció

Màster Oficial de Ciència i Tecnologia Quàntiques / Quantum Science and Technology, Facultat de Física, Universitat de Barcelona. Curs: 2024-2025. Tutors: Arnau Rios Huguet, Javier Rozalén Sarmiento

Matèries

Aprenentatge automàtic, Xarxes neuronals, Treballs de fi de màster

Matèries (anglès)

Machine learning, Neural networks, Master's thesis

Citació

Col·leccions

Màster Oficial - Ciència i Tecnologia Quàntiques / Quantum Science and Technology

Citació

CARRASCO ARANGO, MIguel. Neural Quantum States: Fermions on D-Dimensions. [consulted: 21 of August of 2026]. Available at: https://hdl.handle.net/2445/223230

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