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  • Letter
  • Open Access

Neural network evolution strategy for solving quantum sign structures

Ao Chen1,*, Kenny Choo2, Nikita Astrakhantsev2, and Titus Neupert2

  • 1Department of Physics, ETH Zurich, CH-8093 Zurich, Switzerland
  • 2Department of Physics, University of Zurich, CH-8057 Zurich, Switzerland

  • *chenao.phys@gmail.com
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Phys. Rev. Research 4, L022026 – Published 2 May, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L022026

Abstract

Feed-forward neural networks are a novel class of variational wave functions for correlated many-body quantum systems. Here, we propose a specific neural network ansatz suitable for systems with real-valued wave functions. Its characteristic is to encode the all-important rugged sign structure of a quantum wave function in a convolutional neural network with discrete output. Its training is achieved through an evolutionary algorithm. We test our variational ansatz and training strategy on two spin-1/2 Heisenberg models, one on the two-dimensional square lattice and one on the three-dimensional pyrochlore lattice. In the former, our ansatz converges with high accuracy to the analytically known sign structures of ordered phases. In the latter, where such sign structures are a priori unknown, we obtain better variational energies than with other neural network states. Our results demonstrate the utility of discrete neural networks to solve quantum many-body problems.

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Phys. Rev. Research 4, L022026– Published 2 May, 2022
  • Received 22 November 2021
  • Accepted 22 March 2022
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