Deep learning-enhanced variational Monte Carlo method for quantum many-body physics
Deep learning-enhanced variational Monte Carlo method for quantum many-body physics
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DOI：
10.1103/physrevresearch.2.012039
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发表时间：
2019-05
影响因子：
4.2
通讯作者：
Li Yang;Z. Leng;GuangYuan Yu;Ankit B. Patel;Wenjun Hu;H. Pu
中科院分区：
文献类型：
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作者：
Li Yang;Z. Leng;GuangYuan Yu;Ankit B. Patel;Wenjun Hu;H. Pu
人工神经网络已成功地应用于变分蒙特卡罗方法（VMC）来研究量子多体系统。然而，尽管近年来深度神经网络在许多其他领域取得了巨大成功，但利用深度神经网络（dnn）探索量子多体物理的系统研究却很少。在VMC中实现深度神经网络的一个主要挑战是具有大量参数的网络优化效率低下。引入了一种重要采样梯度优化（ISGO）算法，显著提高了VMC中DNN训练的计算速度。我们设计了一个有效的卷积深度神经网络架构来计算一维（1D） SU（$N$）自旋链的基态。我们对16层深层神经网络的基态能量的数值计算结果与Bethe-Ansatz精确解非常吻合。此外，我们还利用得到的波函数计算了环路相关函数。我们的工作证明了将深度神经网络应用于数值量子多体计算的可行性和优势。
Artificial neural networks have been successfully incorporated into variational Monte Carlo method (VMC) to study quantum many-body systems. However, there have been few systematic studies of exploring quantum many-body physics using deep neural networks (DNNs), despite of the tremendous success enjoyed by DNNs in many other areas in recent years. One main challenge of implementing DNN in VMC is the inefficiency of optimizing such networks with large number of parameters. We introduce an importance sampling gradient optimization (ISGO) algorithm, which significantly improves the computational speed of training DNN in VMC. We design an efficient convolutional DNN architecture to compute the ground state of a one-dimensional (1D) SU($N$) spin chain. Our numerical results of the ground-state energies with up to 16 layers of DNN show excellent agreement with the Bethe-Ansatz exact solution. Furthermore, we also calculate the loop correlation function using the wave function obtained. Our work demonstrates the feasibility and advantages of applying DNNs to numerical quantum many-body calculations.