论文标题
通过恢复对称性，帮助限制了具有量子状态表示的限制性玻尔兹曼机器
Helping restricted Boltzmann machines with quantum-state representation by restoring symmetry
论文作者
论文摘要
基于神经网络的变异波函数最近开始被认为是一种强大的ANSATZ，以准确表示量子多体状态。为了在所有可用的数值方法中显示该方法的有用性，必须研究挑战多体问题的性能，而多体问题则无法确切解决方案。在这里，我们使用最简单的神经网络之一构建了变分波函数，即受限的玻尔兹曼机器（RBM），并将其应用于基本但未解决的量子自旋哈密顿式，二维$ J_1 $ -J_1 $ - $ J_2 $ HEISENBERG在Square Lattice上的Heisenberg型号。我们使用量子数凸起的RBM波函数来恢复波函数的对称性，并可以计算激发态。然后，我们对RBM的性能进行系统的研究。我们表明，在对称性的帮助下，RBM波函数在地面和激发态计算中实现了最先进的精度。该研究显示了关于我们如何以受控方式实现准确性的实用指南。
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 $J_1$-$J_2$ 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.
