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Projector Quantum Monte Carlo Method for Nonlinear Wave Functions.

Lauretta R Schwarz1, A Alavi2, George H Booth3

  • 1University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.

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This summary is machine-generated.

This study introduces a new quantum Monte Carlo method using deep learning for complex wave functions. This approach overcomes exponential scaling issues and improves accuracy for strongly correlated systems like graphene.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Materials Science

Background:

  • Full configuration interaction quantum Monte Carlo (FCI-QMC) methods face exponential scaling challenges.
  • Traditional variational Monte Carlo (VMC) methods use polynomial complex wave functions.
  • Bridging VMC and projector QMC (P-QMC) remains an active research area.

Purpose of the Study:

  • To reformulate projected imaginary-time evolution in FCI-QMC using Lagrangian minimization.
  • To enable the use of polynomial complex wave function parametrizations within QMC.
  • To explore the application of deep learning for optimizing these parametrizations.

Main Methods:

  • Lagrangian minimization of projected imaginary-time evolution.
  • Employing polynomial complex wave function parametrizations.
  • Utilizing deep neural networks to optimize the Lagrangian.
  • Demonstration with tensor network states.

Main Results:

  • Circumvented the exponential scaling of traditional FCI-QMC.
  • Successfully applied the method to the strongly correlated Hubbard model.
  • Demonstrated application to a fully periodic ab initio graphene sheet.
  • Achieved greater optimization variable capacity compared to alternative VMC formulations.

Conclusions:

  • The developed approach blurs the lines between VMC and P-QMC.
  • Offers systematic improvability of wave function flexibility towards exactness.
  • Represents a significant advancement in quantum Monte Carlo methodologies for complex systems.