Recurrent Neural Network Wavefunctions

A core technology that has emerged from the artificial intelligence revolution is the recurrent neural network (RNN). Its unique sequence-based architecture provides a tractable likelihood estimate with stable training paradigms, a combination that has precipitated many spectacular advances in natural language processing and neural machine translation. This architecture also makes a good candidate for a variational wavefunction, where the RNN parameters are tuned to learn the approximate ground state of a quantum Hamiltonian. In this paper, we demonstrate the ability of RNNs to represent several many-body wavefunctions, optimizing the variational parameters using a stochastic approach. Among other attractive features of these variational wavefunctions, their autoregressive nature allows for the efficient calculation of physical estimators by providing perfectly uncorrelated samples. We demonstrate the effectiveness of RNN wavefunctions by calculating ground state energies, correlation functions, and entanglement entropies for several quantum spin models of interest to condensed matter physicists in one and two spatial dimensions.