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

Yusuke Nomura

Research output: Contribution to journalArticlepeer-review

37 Citations (Scopus)


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.

Original languageEnglish
Article number174003
JournalJournal of Physics Condensed Matter
Issue number17
Publication statusPublished - 2021 Apr
Externally publishedYes


  • frustrated spin systems
  • machine learning
  • restricted Boltmann machine
  • variational wave function

ASJC Scopus subject areas

  • General Materials Science
  • Condensed Matter Physics


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