Investigating Topological Order using Recurrent Neural Networks

TL;DR

This paper demonstrates that recurrent neural networks can effectively model and analyze topological order in quantum many-body systems, capturing complex entanglement properties and phase characteristics.

Contribution

The study introduces 2D RNN wave functions as a novel approach to investigate topological phases, successfully applying them to the toric code and kagome lattice spin liquids.

Findings

RNN wave functions accurately estimate topological entanglement entropy.

RNNs favor coherent superpositions of minimally-entangled states.

RNN approach outperforms traditional methods in capturing topological order.

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.