论文标题
用于计算拓扑不变的重新归一化群体启发的神经网络
Renormalization-group-inspired neural networks for computing topological invariants
论文作者
论文摘要
我们表明，鉴于其二维实际空间哈密顿量，人工神经网络（ANN）可以高精度地确定无序系统的拓扑不变。此外，我们描述了一个“重新归一化组”（RG）网络，该网络将大型晶格上的汉密尔顿人转换为另一个小晶格，同时保留不变性。通过迭代将RG网络应用于计算固定尺寸小晶格的Chern数字的“基础”网络，我们可以在不重新训练系统的情况下处理较大的晶格。因此，我们表明，可以针对比网络训练的系统计算更大的系统的真实空间拓扑不变。与以前的方法相比，这为计算时间打开了大门。
We show that artificial neural networks (ANNs) can, to high accuracy, determine the topological invariant of a disordered system given its two-dimensional real-space Hamiltonian. Furthermore, we describe a "renormalization-group" (RG) network, an ANN which converts a Hamiltonian on a large lattice to another on a small lattice while preserving the invariant. By iteratively applying the RG network to a "base" network that computes the Chern number of a small lattice of set size, we are able to process larger lattices without re-training the system. We therefore show that it is possible to compute real-space topological invariants for systems larger than those on which the network was trained. This opens the door for computation times significantly faster and more scalable than previous methods.
