  Recurrent neural networks (RNNs), originally developed for natural language
processing, hold great promise for accurately describing strongly correlated
quantum many-body systems. Here, we employ 2D RNNs to investigate two
prototypical quantum many-body Hamiltonians exhibiting topological order.
Specifically, we demonstrate that RNN wave functions can effectively capture
the topological order of the toric code and a Bose-Hubbard spin liquid on the
kagome lattice by estimating their topological entanglement entropies. We also
find that RNNs favor coherent superpositions of minimally-entangled states over
minimally-entangled states themselves. Overall, our findings demonstrate that
RNN wave functions constitute a powerful tool to study phases of matter beyond
Landau's symmetry-breaking paradigm.
