Nomura Yusuke
RIKEN Center for Emergent Matter Science, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan.
J Phys Condens Matter. 2021 Apr 27;33(17). doi: 10.1088/1361-648X/abe268.
The variational wave functions based on neural networks have recently started to be recognized as a powerful ansatz to represent quantum many-body states accurately. In order to show the usefulness of the method among all available numerical methods, it is imperative to investigate the performance in challenging many-body problems for which the exact solutions are not available. Here, we construct a variational wave function with one of the simplest neural networks, the restricted Boltzmann machine (RBM), and apply it to a fundamental but unsolved quantum spin Hamiltonian, the two-dimensional-Heisenberg model on the square lattice. We supplement the RBM wave function with quantum-number projections, which restores the symmetry of the wave function and makes it possible to calculate excited states. Then, we perform a systematic investigation of the performance of the RBM. We show that, with the help of the symmetry, the RBM wave function achieves state-of-the-art accuracy both in ground-state and excited-state calculations. The study shows a practical guideline on how we achieve accuracy in a controlled manner.
基于神经网络的变分波函数最近开始被认为是一种能够精确表示量子多体状态的强大假设。为了在所有可用的数值方法中展示该方法的实用性，研究其在没有精确解的具有挑战性的多体问题中的性能势在必行。在这里，我们用最简单的神经网络之一——受限玻尔兹曼机（RBM）构建一个变分波函数，并将其应用于一个基本但未解决的量子自旋哈密顿量，即方形晶格上的二维海森堡模型。我们用量子数投影来补充RBM波函数，这恢复了波函数的对称性并使得计算激发态成为可能。然后，我们对RBM的性能进行了系统研究。我们表明，借助对称性，RBM波函数在基态和激发态计算中都达到了当前的最高精度。该研究展示了如何以可控方式实现精度的实用指导方针。
