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.

翻译：递归神经网络（RNN）最初为自然语言处理而开发，在精确描述强关联量子多体系统方面展现出巨大潜力。本文采用二维RNN研究两个具有拓扑序的典型量子多体哈密顿量。具体而言，通过估计拓扑纠缠熵，我们证明RNN波函数能够有效捕捉环面码和Kagome晶格上Bose-Hubbard自旋液体的拓扑序。同时发现，RNN倾向于支持最小纠缠态的相干叠加而非最小纠缠态本身。总体而言，我们的研究结果表明，RNN波函数是研究超越朗道对称性破缺范式的物质相的有力工具。