Neural network wave functions for superfluid fermi gases
Author(s)
Lou, Wan Tong
Type
Thesis or dissertation
Abstract
The search for exotic phases of matter in quantum systems remains a central goal in condensed matter physics. Recent progress in machine learning has driven the development of powerful new computational methods in quantum chemistry and physics. In particular, the application of neural networks to solve the Schrödinger equation within the variational Monte Carlo (VMC) framework has led to the development of the successful neural network VMC (NNVMC) method. This thesis extends and explores the application of NNVMC to the study of strongly interacting Fermi gases.
We first investigated the unitary Fermi gas (UFG)---a system with strong, short-range attractions known to possess a superfluid ground state that is difficult to describe quantitatively. By applying the NNVMC method with the FermiNet Ansatz, we first identified its key limitations before proposing a simple modification. This change led to a substantial improvement in accuracy over the original FermiNet in the UFG, outperforming results from the state-of-the-art simulations while being consistent with experiments.
Next, we explored the phases of the 2D spin-imbalanced Fermi gas. The combined power of NNVMC and our modified FermiNet enabled us not only to observe the long-predicted Fulde-Ferrell-Larkin-Ovchinnikov phase but also to discover a previously unknown phase, characterised by the crystallisation of tightly bound Cooper pairs within a uniform sea of unpaired fermions.
Lastly, we studied an anisotropic Fermi gas featuring spin-dependent splitting in momentum space --- a prime signature of the recently discovered form of collinear magnetism, termed altermagnetism. We mapped its 2D phase diagram, providing unbiased estimations for the locations of various phases beyond the mean-field approximation.
In conclusion, our work has demonstrated that the NNVMC method is a powerful and versatile tool for investigating strongly correlated systems, confirming its potential to uncover novel phenomena in the vast landscape of quantum systems.
We first investigated the unitary Fermi gas (UFG)---a system with strong, short-range attractions known to possess a superfluid ground state that is difficult to describe quantitatively. By applying the NNVMC method with the FermiNet Ansatz, we first identified its key limitations before proposing a simple modification. This change led to a substantial improvement in accuracy over the original FermiNet in the UFG, outperforming results from the state-of-the-art simulations while being consistent with experiments.
Next, we explored the phases of the 2D spin-imbalanced Fermi gas. The combined power of NNVMC and our modified FermiNet enabled us not only to observe the long-predicted Fulde-Ferrell-Larkin-Ovchinnikov phase but also to discover a previously unknown phase, characterised by the crystallisation of tightly bound Cooper pairs within a uniform sea of unpaired fermions.
Lastly, we studied an anisotropic Fermi gas featuring spin-dependent splitting in momentum space --- a prime signature of the recently discovered form of collinear magnetism, termed altermagnetism. We mapped its 2D phase diagram, providing unbiased estimations for the locations of various phases beyond the mean-field approximation.
In conclusion, our work has demonstrated that the NNVMC method is a powerful and versatile tool for investigating strongly correlated systems, confirming its potential to uncover novel phenomena in the vast landscape of quantum systems.
Date Issued
2025-10-02
Date Awarded
2026-02-01
Copyright Statement
Attribution-NonCommercial 4.0 International Licence (CC BY-NC)
License URL
Advisor
Foulkes, William
Knolle, Johannes
Sponsor
Imperial College London
Publisher Department
Department of Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)