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.

使用卷积神经网络模型作为变分 ansatz，研究了二维受挫磁体的模型，证明了所得结果与现有的最先进方法相当甚至更好。