Investigating Topological Order using Recurrent Neural Networks

Abstract

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.

15 pages, 6 figures, 2 tables. Published version in Physical Review B

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• Array Programming with NumPy
• Identifying Topological Order by Entanglement Entropy
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Ground state entanglement and geometric entropy in the Kitaev's model
• Variational neural network ansatz for steady states in open quantum systems
• Quantum phases of Rydberg atoms on a kagome lattice
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• Impact of conditional modelling for a universal autoregressive quantum state
• Recurrent neural network wave functions for Rydberg atom arrays on kagome lattice
• Design principles of deep translationally-symmetric neural quantum states for frustrated magnets
• ParaToric 1.0: Continuous-time quantum Monte Carlo for the toric code in a parallel field
• Topological Order in Neural Wavefunctions
• Emergence of global receptive fields capturing multipartite quantum correlations
• The statistical mechanics and machine learning of the $\alpha$-Rényi ensemble
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