论文标题
深入学习功能重新归一化组
Deep Learning the Functional Renormalization Group
论文作者
论文摘要
我们对广泛研究的二维$ t-t'$ hubbard模型的功能重新归一化组（FRG）流动的比例依赖性4点顶点函数进行了数据驱动的维度降低。我们证明，在低维潜在空间中基于神经常规微分方程求解器的深度学习架构有效地学习了划定哈伯德模型的各种磁性和$ d $ - 波 - 波 - 波的超导态度的动力学。我们进一步提出了动态模式分解分析，该分析确认少数模式确实足以捕获FRG动力学。我们的工作证明了使用人工智能提取相关电子的4点顶点函数的紧凑表示的可能性，这对于成功解决多电子问题的最重要的量子场理论方法是最重要的目标。
We perform a data-driven dimensionality reduction of the scale-dependent 4-point vertex function characterizing the functional Renormalization Group (fRG) flow for the widely studied two-dimensional $t - t'$ Hubbard model on the square lattice. We demonstrate that a deep learning architecture based on a Neural Ordinary Differential Equation solver in a low-dimensional latent space efficiently learns the fRG dynamics that delineates the various magnetic and $d$-wave superconducting regimes of the Hubbard model. We further present a Dynamic Mode Decomposition analysis that confirms that a small number of modes are indeed sufficient to capture the fRG dynamics. Our work demonstrates the possibility of using artificial intelligence to extract compact representations of the 4-point vertex functions for correlated electrons, a goal of utmost importance for the success of cutting-edge quantum field theoretical methods for tackling the many-electron problem.
