Neural Networks for Analytic Continuation of Response Functions*

In the last few years, it was shown that deep neural networks can outperform Maximum Entropy methods for the analytical continuation of noisy Matsubara Green’s function [1,2,3,4]. Extending these tools to correlation function for transport quantities would be beneficial because, in some cases, such as Hall conductivity and Seebeck effect [5,6], the spectral weight is not strictly positive, restricting the use of the maximum entropy method. In this work, we extend the use of deep neural networks to the case of the longitudinal conductivity, in particular the DC conductivity. We also introduce a rescaling procedure that allows trained networks to generalize to all temperatures.
[1] Fournier et al. arXiv:1810.00913 (2018).
[2] Yoon et al. Phys. Rev. B 98, 245101 (2018).
[3] Kades et al. arXiv:1905.04305 (2019).
[4] Xie et al. arXiv:1905.10430 (2019).
[5] Verret et al. Phys. Rev. B 96, 125139 (2017).
[6] Nourafkan & Tremblay Phys. Rev. B 98, 165130 (2018).