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Fermionic wave functions from neural-network constrained hidden states.

Javier Robledo Moreno1,2, Giuseppe Carleo3,4, Antoine Georges1,5,6,7

  • 1Center for Computational Quantum Physics, Flatiron Institute, New York, NY 10010.

Proceedings of the National Academy of Sciences of the United States of America
|August 3, 2022
PubMed
Summary
This summary is machine-generated.

We developed a new variational wave function method for simulating strongly correlated fermionic systems. This approach uses neural networks and hidden particles to achieve highly accurate results for complex models.

Keywords:
electronic structurefermionsneural networksquantum physicsvariational Monte Carlo

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Area of Science:

  • Quantum mechanics
  • Computational physics
  • Materials science

Background:

  • Simulating strongly correlated fermionic systems is computationally challenging.
  • Existing methods often struggle with accuracy for complex electronic structures.
  • Variational methods offer a promising avenue but require expressive wave functions.

Purpose of the Study:

  • To introduce a novel, systematically improvable family of variational wave functions.
  • To overcome limitations of previous hidden-particle approaches.
  • To achieve highly accurate simulations of fermionic systems.

Main Methods:

  • Constructing wave functions using Slater determinants in an augmented Hilbert space.
  • Incorporating "hidden" fermionic degrees of freedom.
  • Optimizing constraints and orbitals with neural network parameterization.

Main Results:

  • Demonstrated a universal and extremely expressive family of wave functions.
  • Applied the method to the Hubbard model on a square lattice.
  • Achieved accuracy competitive with state-of-the-art variational methods.

Conclusions:

  • The proposed method offers a powerful new tool for strongly correlated systems.
  • Neural network parameterization enhances the expressiveness and accuracy of variational wave functions.
  • This approach paves the way for more precise simulations in condensed matter physics.