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Discovering Quantum Phase Transitions with Fermionic Neural Networks.

Gino Cassella1, Halvard Sutterud1, Sam Azadi2

  • 1Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom.

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Summary
This summary is machine-generated.

FermiNet, a deep neural network, accurately calculates ground states for periodic systems like the homogeneous electron gas. It captures both delocalized and localized states, even predicting phase transitions without prior knowledge.

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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.