Neural network evolution strategy for solving quantum sign structures

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.

Automated summary

In this study, a neural network method suitable for systems with real-valued wave functions is proposed, encoding the sign structure of a quantum wave function in a convolutional neural network with discrete output. The training is achieved through an evolutionary algorithm. The results demonstrate that this method can accurately converge to the known sign structures of ordered phases and obtain better variational energies compared to other neural network states in cases where the sign structures are a priori unknown.