Investigating Topological Order using Recurrent Neural Networks
This work provides a new computational tool for physicists studying exotic phases of matter beyond traditional symmetry-breaking paradigms, though it is incremental in applying existing RNN methods to quantum systems.
The researchers tackled the problem of describing strongly correlated quantum many-body systems with topological order by using 2D recurrent neural networks (RNNs), demonstrating that RNN wave functions can effectively capture topological order in the toric code and a Bose-Hubbard spin liquid on the kagome lattice by estimating topological entanglement entropies.
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.