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Frontiers in artificial intelligence and applications

Finding Quantum Critical Points with Neural-Network Quantum States

Remmy A. M. Zen, My Long, Tan Ryan, F. Hébert, M. Gattobigio, Christian Miniatura, Dario Poletti, Stéphane Bressan

Published Jan 1, 2020• 0 citations
Publisher
DOI
10.3233/faia200315

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Abstract We study the Rényi entropy in a one-dimensional transverse-field quantum Ising model by virtue of the machine learning methods with neural networks. The Rényi entropy is investigated both in the static ground state and in the dynamical state after a linear quench, by employing a swapping operator acting on the states prepared from the neural networks. In the ground state, the behavior of Rényi entropy can unveil the critical point from paramagnetic to ferromagnetic phase. At the critical point, the relation between the Rényi entropy and the subsystem size from the machine learning method satisfies the predictions from conformal field theory. In the quenching dynamics, coherent oscillations of the Rényi entropy are observed after the end of the quench. These oscillations have universal frequencies stem from the superpositions of the excited states. More importantly, an asymptotic scaling of the reduced Rényi entropy is observed, implying a novel length scale away from the critical point.
Predicting the phase diagram of interacting quantum many-body systems is a central problem in condensed matter physics and related fields. A variety of quantum many-body systems, ranging from unconventional superconductors to spin liquids, exhibit complex competing phases whose theoretical description has been the focus of intense efforts. Here, we show that neural network quantum states can be combined with a Lee-Yang theory of quantum phase transitions to predict the critical points of strongly correlated spin lattices. Specifically, we implement our approach for quantum phase transitions in the transverse-field Ising model on different lattice geometries in one, two, and three dimensions. We show that the Lee-Yang theory combined with neural network quantum states yields predictions of the critical field, which are consistent with large-scale quantum many-body methods. As such, our results provide a starting point for determining the phase diagram of more complex quantum many-body systems, including frustrated Heisenberg and Hubbard models.