Deep learning approach for quantum many-body systems

Author(s)

William Freitas e Silva

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Física Gleb Wataghin
• Defense date: 2024-08-30

Examining board members

Silvio Antonio Sachetto Vitiello; Lucas Madeira; Maurice de Koning; Ricardo Luís Doretto; Von Braun Nascimento

• Advisor: Silvio Antonio Sachetto Vitiello

Abstract

In the field of quantum mechanics, the description of quantum states is fundamental to explain and predict the behaviour of finite systems. One strategy to accomplish this is through the variational method, where the quantum states are described by trial wave functions. Moreover, the striking resemblance between deep learning algorithms and the variational method suggests that trial functions can be represented by artificial neural networks. Hence, this representation was employed in this work to analyse systems composed of bosons, such as helium-4 clusters, and fermions, such as quantum dots. By using Monte Carlo integration to compute the relevant integrals and by training the neural network to find the ground state energy of these systems, the yielded results reached unprecedented accuracy compared with quantum Monte Carlo methods. While those methods produce robust statistical values for the energy of bosonic systems, it requires extrapolation for quantities that do not commute with the Hamiltonian, potentially introducing bias. Therefore, aiming to circumvent extrapolations, the neural network representation of ground states was employed to compute several properties such as density profiles, pair distribution functions, and pair density functions. Moreover, short range correlations in the context of weak universality for helium clusters was investigated. Also, in order to understand the success of neural networks describing quantum systems, properties of scaling the size of the network and the nodal structure of the optimised trial functions were analysed for quantum dots (AU)

• FAPESP's process: 20/10505-6 - Deep learning approach for quantum many-body physics
• Grantee: William Freitas e Silva
• Support Opportunities: Scholarships in Brazil - Doctorate