Analytical continuation of transport functions with deep neural networks*

In the last few years, deep neural networks have proved to be highly efficient tools to address the problem of analytical continuation of the Matsubara Green’s function [1,2,3,4]. Extending these tools to reconstruct spectral representation of correlation function for transport quantities would be very beneficial because for several of transport quantities, 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 explore various modern architectures of neural network and various tailored-made loss functions for this problem.
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[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).