Properties and Computational Analysis of Quantum Nanosystems: Harmonic Confinement and Machine Learning Methods in Hubbard Models

• Grant number: 25/13615-0
• Support Opportunities: Regular Research Grants
• Start date: November 01, 2025
• End date: October 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Chemistry
• Principal Investigator: Vivian Vanessa França Henn
• Grantee: Vivian Vanessa França Henn
• Host Institution: Instituto de Química (IQ). Universidade Estadual Paulista (UNESP). Campus de Araraquara. Araraquara , SP, Brazil
• City of the host institution: Araraquara
• Associated research grant: 21/06744-8 - Quantum phase transitions in nanomaterials: developing of density functionals and their applications via DFT, AP.JP2
• Associated scholarship(s): 25/22271-3 - Properties of Nanosystems with Harmonic Confinement: A Study via Density Functional Theory, BP.IC; 25/22628-9 - Application of Machine Learning Methods to the Study of Disordered Nanosystems, BP.IC

Abstract

One-dimensional quantum nanosystems modeled by the Hubbard Hamiltonian exhibit a rich range of physical phenomena, including effects of harmonic confinement and disorder-induced transitions such as Anderson localization. These systems are central to Theoretical Chemistry, Condensed Matter Physics, and Materials Science, with promising applications in quantum nanoscale devices. This project proposes an integrated computational approach: on one hand, to investigate the physical properties-energy, electronic density, magnetization, and quantum entanglement-of harmonically confined chains using Density Functional Theory (DFT); on the other hand, to apply machine learning techniques to reduce the computational cost associated with the study of disordered systems by identifying relevant physical patterns from smaller datasets. The student will be trained in advanced theoretical and computational methods, developing critical analysis skills for results interpretation and contributing to the understanding of strongly correlated and disordered quantum systems. (AU)