Discovering Quantum Phase Transitions with Fermionic Neural Networks

Area of Science:

• Computational Quantum Chemistry
• Materials Science
• Artificial Intelligence in Physics

Background:

• Deep neural networks, like FermiNet, have shown success as accurate wave function Ansätze for variational Monte Carlo (VMC) calculations of molecular ground states.
• Extending these methods to periodic systems is crucial for understanding condensed matter physics and materials science.
• The homogeneous electron gas (HEG) is a fundamental model system for studying electron correlation effects in solids.

Purpose of the Study:

• To extend the FermiNet deep neural network Ansatz for accurate ground-state calculations of periodic Hamiltonians.
• To investigate the application of FermiNet to the homogeneous electron gas (HEG) and compare its performance with established quantum Monte Carlo methods.
• To explore FermiNet's capability in describing different electronic phases, including the Fermi liquid and Wigner crystal states, and its ability to capture phase transitions.

Main Methods:

• Extension of the FermiNet deep neural network architecture to handle periodic boundary conditions for crystalline systems.
• Application of the extended FermiNet to calculate ground-state energies of the homogeneous electron gas across various densities.
• Comparison of FermiNet results with high-accuracy initiator full configuration interaction quantum Monte Carlo (i-FCIQMC) and diffusion Monte Carlo (DMC) calculations.

Main Results:

• FermiNet calculations for the homogeneous electron gas show excellent agreement with state-of-the-art quantum Monte Carlo methods for ground-state energies.
• The neural network architecture successfully describes both the delocalized Fermi liquid state at high electron densities and the localized Wigner crystal state at low densities.
• FermiNet spontaneously breaks symmetry to converge on the crystalline ground state at low density, accurately predicting the phase transition without explicit prior information.

Conclusions:

• The extended FermiNet is a highly accurate and versatile Ansatz for variational Monte Carlo calculations of ground states in periodic systems.
• Deep neural networks can effectively capture complex electronic phases and phase transitions in condensed matter systems.
• This work demonstrates the potential of machine learning methods to advance the study of quantum many-body problems in physics and chemistry.