Helping restricted Boltzmann machines with quantum-state representation by restoring symmetry

• Published in: Journal of physics. Condensed matter 2021-04, Vol.33 (17), p.174003
• Main Author: Nomura, Yusuke
• Format: Article
• Language: English
• Subjects: frustrated spin systems; machine learning; restricted Boltmann machine; variational wave function
• ISSN: 0953-8984; 1361-648X
• DOI: 10.1088/1361-648X/abe268

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 - 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.