We develop a reliable parameter-free analytic continuation method for quantum many-body calculations. Our method is based on a kernel grid, a causal spline, a regularization using the second-derivative roughness penalty, and the L-curve criterion. We also develop the L-curve averaged deviation to estimate the precision of our analytic continuation. To deal with statistically obtained data more efficiently, we further develop a bootstrap-averaged analytic continuation method. In the test using the exact imaginary-frequency Green's function with added statistical error, our method produces the spectral function that converges systematically to the exact one as the statistical error decreases. As an application, we simulate the two-orbital Hubbard model for various electron numbers with the dynamical-mean field theory in the imaginary time and obtain the real-frequency self-energy with our analytic continuation method, clearly identifying a non-Fermi liquid behavior as the electron number approaches the half filling from the quarter filling. Our analytic continuation can be used widely and it will facilitate drawing clear conclusions from imaginary-time quantum many-body calculations.
Training biases in machine learning for the analytic continuation of quantum many-body Green's functions
我们解决的问题解析连续的频率格林函数，这是至关重要的多体物理，使用机器学习的基础上的多级残差神经网络。我们专门解决潜在的偏见，可以引入由于使用人工创建的频谱函数，用于训练神经网络。我们还基于Monte Carlo dropout实现了预测谱函数的不确定性估计，这允许识别预测可能不准确的频率区域，并且我们研究了噪声的影响，特别是对于训练期间的噪声水平与实际数据不同的情况。我们的分析表明，这种方法确实可以实现高质量的预测，与广泛使用的最大熵方法相当或更好，但目前由于缺乏可用于训练的真实数据，进一步的改进受到限制。我们还基准我们的方法，通过将其应用到SrVO $_3$的情况下，其中一个准确的谱函数已获得从动态平均场论使用求解器，直接在实际频率轴上工作。
Analytical Singular-Value Structure of Analytic-Continuation Kernels from Slepian Information Theory
Graduate School of Information Sciences, Tohoku University（东北大学信息科学研究院）；Department of Physics, Institute of Science Tokyo（东京科学大学物理系）；Research and Education Institute for Semiconductors and Informatics, Kumamoto University（熊本大学半导体与信息学研究与教育学院）；Sigma-i Co., Ltd.（Sigma-i有限公司）
