Investigating Topological Order using Recurrent Neural Networks

• URL: http://arxiv.org/abs/2303.11207v3
• Date: Wed, 25 Oct 2023 23:32:02 GMT
• Title: Investigating Topological Order using Recurrent Neural Networks
• Authors: Mohamed Hibat-Allah, Roger G. Melko, Juan Carrasquilla
• Abstract summary: 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.
• Score: 0.7234862895932991
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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