Restricted Boltzmann machine learning for solving strongly correlated quantum systems

Yusuke Nomura, Andrew S. Darmawan, Youhei Yamaji, Masatoshi Imada

Research output: Contribution to journalArticlepeer-review

184 Citations (Scopus)


We develop a machine learning method to construct accurate ground-state wave functions of strongly interacting and entangled quantum spin as well as fermionic models on lattices. A restricted Boltzmann machine algorithm in the form of an artificial neural network is combined with a conventional variational Monte Carlo method with pair product (geminal) wave functions and quantum number projections. The combination allows an application of the machine learning scheme to interacting fermionic systems. The combined method substantially improves the accuracy beyond that ever achieved by each method separately, in the Heisenberg as well as Hubbard models on square lattices, thus proving its power as a highly accurate quantum many-body solver.

Original languageEnglish
Article number205152
JournalPhysical Review B
Issue number20
Publication statusPublished - 2017 Nov 29
Externally publishedYes

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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