Backflow Transformations via Neural Networks for Quantum Many-Body Wave Functions.

Area of Science:

• Quantum Many-Body Physics
• Computational Physics
• Machine Learning in Physics

Background:

• Accurate ground state wave functions are crucial for solving quantum many-body problems.
• Traditional methods often struggle with the complexity of these systems.
• The backflow approach offers a way to improve mean-field states by adding correlations.

Purpose of the Study:

• To propose a new class of wave functions called neural network backflow (NNB).
• To leverage machine learning for optimizing wave function transformations.
• To enhance the accuracy and properties of quantum ground states.

Main Methods:

• Utilizing feed-forward neural networks to learn optimal orbital transformations.
• Employing variational Monte Carlo calculations for optimization.
• Benchmarking NNB on Hubbard models at intermediate doping.

Main Results:

• NNB significantly reduces relative error in simulations.
• The method restores symmetry to observables and single-particle orbitals.
• NNB effectively decreases double-occupancy density and alters wave function sign structure.

Conclusions:

• Neural network backflow provides a powerful and systematically improvable method for quantum many-body problems.
• NNB generalizes and enhances existing backflow techniques.
• The optimized neural network reveals interesting patterns in its weights and biases.