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The use of artificial neural networks to represent quantum wave-functions hasrecently attracted interest as a way to solve complex many-body problems. Thepotential of these variational parameterizations has been supported byanalytical and numerical evidence in controlled benchmarks. While approachingthe end of the early research phase in this field, it becomes increasinglyimportant to show how neural-network states perform for models and physicalproblems that constitute a clear open challenge for other many-bodycomputational methods. In this paper we start addressing this aspect,concentrating on a presently unsolved model describing two-dimensionalfrustrated magnets. Using a fully convolutional neural network model as avariational ansatz, we study the frustrated spin-1/2 J1-J2 Heisenberg model onthe square lattice. We demonstrate that the resulting predictions for bothground-state energies and properties are competitive with, and often improveupon, existing state-of-the-art methods. In a relatively small region in theparameter space, corresponding to the maximally frustrated regime, our ansatzexhibits comparatively good but not best performance. The gap between thecomplexity of the models adopted here and those routinely adopted in deeplearning applications is, however, still substantial, such that furtherimprovements in future generations of neural-network quantum states are likelyto be expected.

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