Two-dimensional frustrated J1-J2 model studied with neural network quantum states
Two-dimensional frustrated J1-J2 model studied with neural network quantum states
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DOI：
10.1103/physrevb.100.125124
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发表时间：
2019-09-11
影响因子：
3.7
通讯作者：
Carleo, Giuseppe
中科院分区：
文献类型：
--
作者：
Choo, Kenny;Neupert, Titus;Carleo, Giuseppe
使用人工神经网络来表示量子波函数作为一种解决复杂多体问题的方法最近引起了人们的兴趣。这些变分参数化的潜力已被控制基准的分析和数值证据所支持。当该领域的早期研究阶段接近尾声时，展示神经网络状态如何处理模型和物理问题变得越来越重要，这些问题对其他多体计算方法构成了明确的公开挑战。在本文中，我们开始解决这方面，集中在一个目前尚未解决的模型描述二维受挫磁铁。利用全卷积神经网络模型作为变分分析，研究了方形晶格上受挫自旋-1/2 J(1)-J(2)海森堡模型。我们证明，对基态能量和性质的预测结果与现有的最先进的方法相竞争，并且经常改进。在参数空间中相对较小的区域，对应于最大受挫状态，我们的ansatz表现出相对较好的性能，但不是最好的性能。然而，这里采用的模型的复杂性与深度学习应用中常规采用的模型之间的差距仍然很大，因此，未来几代神经网络量子态的进一步改进可能是可以预期的。
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 parametrizations 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 J(1)-J(2) 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 the 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.