Journal
JOURNAL OF PHYSICS-CONDENSED MATTER
Volume 33, Issue 17, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/1361-648X/abe268
Keywords
restricted Boltmann machine; variational wave function; frustrated spin systems; machine learning
Categories
Funding
- JSPS KAKENHI [16H06345, 17K14336, 18H01158, 20K14423]
- MEXT
- Grants-in-Aid for Scientific Research [17K14336, 18H01158, 20K14423] Funding Source: KAKEN
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The article introduces a variational wave function method based on neural networks, showing excellent performance in solving quantum many-body state problems. By supplementing quantum-number projections to restore symmetry in the RBM wave function, state-of-the-art accuracy is achieved in both ground-state and excited-state calculations. The study provides a practical guideline for achieving accuracy in a controlled manner.
The variational wave functions based on neural networks have recently started to be recognized as a powerful ansatz to represent quantum many-body states accurately. In order to show the usefulness of the method among all available numerical methods, it is imperative to investigate the performance in challenging many-body problems for which the exact solutions are not available. Here, we construct a variational wave function with one of the simplest neural networks, the restricted Boltzmann machine (RBM), and apply it to a fundamental but unsolved quantum spin Hamiltonian, the two-dimensional J (1)-J (2) Heisenberg model on the square lattice. We supplement the RBM wave function with quantum-number projections, which restores the symmetry of the wave function and makes it possible to calculate excited states. Then, we perform a systematic investigation of the performance of the RBM. We show that, with the help of the symmetry, the RBM wave function achieves state-of-the-art accuracy both in ground-state and excited-state calculations. The study shows a practical guideline on how we achieve accuracy in a controlled manner.
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