AI 中文总结
该研究为机器学习引入实频谱函数的紧凑稳定矩表示，由凯莱映射三角矩构建，保持谱权重归一化等。通过图注意力神经网络在多种模型上测试，结果显示精度高，能可靠再现相关物理量，实现稳定自能重构及准确恢复矩阵值谱。
AI 中文摘要
我们为机器学习应用引入了一种用于实频格林函数、杂化函数和自能的紧凑稳定矩表示，避免了密集频率网格的低效率以及松原方法的不适定解析延拓。该表示由包含雅可比行列式的凯莱映射三角矩构建而成，它保持谱权重归一化，将矩序列与正矩阵值谱测度联系起来，并通过ESPRIT提供了一条通往极点表示的系统途径。这提供了一个固定维度的学习目标，其中诸如归一化和正性等物理约束可以直接施加。我们使用具有FiLM条件的图注意力神经网络，在单轨道DMFT、反铁磁DMFT和双轨道杂质模型上对该表示进行基准测试。结果表明，其精度与直接频域学习相当或更高，能可靠地再现密度和交错磁化强度，通过戴森方程反演实现稳定的自能重构，并能准确恢复具有轨道混合的矩阵值谱。
英文摘要
We introduce a compact and stable moment representation for real-frequency Green's functions, hybridization functions, and self-energies for machine-learning applications, avoiding the inefficiency of dense frequency grids as well as the ill-posed analytic continuation of Matsubara approaches. The representation is constructed from Cayley-mapped trigonometric moments with the Jacobian included, which preserve spectral-weight normalization, tie the moment sequence to a positive matrix-valued spectral measure, and admit a systematic route to a pole representation via ESPRIT. This provides a fixed-dimensional learning target in which physical constraints such as normalization and positivity can be imposed directly. Using a graph-attention neural network with FiLM conditioning, we benchmark the representation on single-orbital DMFT, antiferromagnetic DMFT, and a two-orbital impurity model. The results demonstrate accuracy matching or exceeding that of direct frequency-domain learning, reliable reproduction of the density and staggered magnetization, stable self-energy reconstruction through Dyson equation inversion, and accurate recovery of matrix-valued spectra with orbital mixing.
