Study of the Two-Dimensional Frustrated J1-J2 Model with Neural Network Quantum States

The use of artificial neural networks to represent quantum wave-functions has recently attracted interest as a way to solve complex many-body problems. The potential of these variational parameterizations has been supported by analytical and numerical evidence in controlled benchmarks. While approaching the end of the early research phase in this field, it becomes increasingly important to show how neural-network states perform for models and physical problems that constitute a clear open challenge for other many-body computational methods. In this paper we start addressing this aspect, concentrating on a presently unsolved model describing two-dimensional frustrated magnets. Using a fully convolutional neural network model as a variational ansatz, we study the frustrated spin-1/2 J1-J2 Heisenberg model on the square lattice. We demonstrate that the resulting predictions for both ground-state energies and properties are competitive with, and often improve upon, existing state-of-the-art methods. In a relatively small region in the parameter space, corresponding to the maximally frustrated regime, our ansatz exhibits comparatively good but not best performance. The gap between the complexity of the models adopted here and those routinely adopted in deep learning applications is, however, still substantial, such that further improvements in future generations of neural-network quantum states are likely to be expected.