Hybrid convolutional neural network and projected entangled pair states wave functions for quantum many-particle states

Neural networks have been used as variational wave functions for quantum many-particle problems. It has been shown that the correct sign structure is crucial to obtain highly-accurate ground state energies. In this paper, we propose a hybrid wave function combining the convolutional neural network (CNN) and projected entangled pair states (PEPS), in which the sign structures are determined by the PEPS, and the amplitudes of the wave functions are provided by CNN. We benchmark the ansatz on the highly frustrated spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model. We show that the achieved ground energies are competitive with state-of-the-art results.