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Solving the nuclear pairing model with neural network quantum states
Mauro Rigo1, Benjamin Hall2,3, Morten Hjorth-Jensen2,4
1Physics Department, University of Trento, via Sommarive 14, I-38123 Trento, Italy.
Physical Review. E
|March 18, 2023
Summary
We developed a new variational Monte Carlo method using artificial neural networks to solve the nuclear many-body problem. This approach accurately predicts nuclear energies, outperforming traditional methods like coupled-cluster.
Area of Science:
- Computational Physics
- Nuclear Physics
- Quantum Many-Body Theory
Background:
- The nuclear many-body problem is computationally intensive.
- Accurate solutions are crucial for understanding nuclear structure and interactions.
- Existing methods like coupled-cluster have limitations.
Purpose of the Study:
- To develop a novel variational Monte Carlo (VMC) method for the nuclear many-body problem.
- To utilize artificial neural networks (ANNs) for representing the ground-state wave function.
- To train the ANN efficiently using a memory-efficient stochastic reconfiguration algorithm.
Main Methods:
- Variational Monte Carlo (VMC) method.
- Occupation number formalism.
- Artificial neural network (ANN) representation of the ground-state wave function.
- Stochastic reconfiguration algorithm for network training.
Main Results:
- The VMC-ANN method was benchmarked against established nuclear many-body techniques.
- It accurately described nuclear pairing phenomena for various interactions and strengths.
- The method demonstrated polynomial computational cost.
- Energies obtained were in excellent agreement with full configuration-interaction (FCI) values.
- Performance surpassed coupled-cluster methods.
Conclusions:
- The proposed VMC-ANN method offers a powerful and efficient approach to solving the nuclear many-body problem.
- It provides highly accurate ground-state energies.
- This method shows significant promise for future nuclear structure calculations.
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