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

## TL;DR

This paper explores the application of convolutional neural networks to model the two-dimensional frustrated J1-J2 Heisenberg spin system, showing competitive results and highlighting the potential for future improvements in neural-network quantum states.

## Contribution

It demonstrates the effectiveness of neural network quantum states in tackling a complex, unsolved two-dimensional frustrated magnet model, advancing the application of deep learning in quantum many-body physics.

## Key findings

- Neural network states achieve competitive ground-state energy predictions.
- Performance is particularly strong outside the maximally frustrated regime.
- Further improvements are expected with more advanced neural network architectures.

## Abstract

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.