Restricted-Boltzmann-Machine Learning for Solving Hubbard and Heisenberg Models

We propose a versatile machine learning technique to construct accurate ground state wave functions of strongly-entangled spin/boson systems as well as fermionic lattice models [1]. We construct a variational wave function, which we call RBM+PP, by combining concepts from machine learning (restricted Boltzmann machine (RBM)) and physics (pair-product (PP) wave functions). The RBM is a type of artificial neural networks, allowing for a flexible and unbiased description of a wide variety of quantum states. The PP wave function or geminal wave function used in conventional wave-function methods such as the variational Monte Carlo (VMC) method, properly describes nonlocal entanglement, helping machine learning to learn many-body ground states more efficiently. Combined RBM+PP substantially improves accuracies of the RBM and VMC method applied separately in Heisenberg and Hubbard models. The high accuracy and flexible applicability of the RBP+PP wave function opens up a new route in the study of strongly-correlated systems. [1] Y. Nomura, A. Darmawan, Y. Yamaji, and M. Imada, arXiv:1709.06475.