论文标题
Hubbardnet：具有深神经网络的Bose-Hubbard模型频谱的有效预测
HubbardNet: Efficient Predictions of the Bose-Hubbard Model Spectrum with Deep Neural Networks
论文作者
论文摘要
我们提出了一个基于深的神经网络（DNN）的模型（Hubbardnet），以变化找到一维和二维Bose-Hubbard模型的基态和激发态波形。将此模型用于带有$ M $站点的方格，我们从单个培训中获得了现场库仑排斥，$ u $的分析功能，$ u $ $ u $，$ n $的总数。这种方法绕过了为每组不同的值$（u，n）$解决新的哈密顿量的需求。使用\ texttt {hubbardnet}，我们确定了Bose-Hubbard模型（Mott Insulator和Superfluid）的两个基态阶段。我们表明，DNN候选化溶液与哈密顿量确切的对角线化的结果非常吻合，并且在计算缩放方面的表现优于精确的对角线化。这些优势表明，我们的模型有望有望有效，准确地计算多体晶格汉密尔顿人的精确相图。
We present a deep neural network (DNN)-based model (HubbardNet) to variationally find the ground state and excited state wavefunctions of the one-dimensional and two-dimensional Bose-Hubbard model. Using this model for a square lattice with $M$ sites, we obtain the energy spectrum as an analytical function of the on-site Coulomb repulsion, $U$, and the total number of particles, $N$, from a single training. This approach bypasses the need to solve a new hamiltonian for each different set of values $(U,N)$. Using \texttt{HubbardNet}, we identify the two ground state phases of the Bose-Hubbard model (Mott insulator and superfluid). We show that the DNN-parametrized solutions are in excellent agreement with results from the exact diagonalization of the hamiltonian, and it outperforms exact diagonalization in terms of computational scaling. These advantages suggest that our model is promising for efficient and accurate computation of exact phase diagrams of many-body lattice hamiltonians.
