Maximum quantum entropy method: the analytic continuation of matrix-valued Green's functions

Analytic continuation of the quantum Monte Carlo data written in the imaginary-frequency to the real-frequency axis is one of the difficult numeric problems, due to the ill-conditioned nature of the kernel matrix. While the maximum entropy method (MEM) is one of the most suitable choices to gain information from the noisy input data, its applications are limited by the non-negative condition of the output spectral function. Here we have extended the MEM to the matrix-valued function, introducing quantum relative entropy as a regularization function [1]. As a true matrix-valued method, our maximum quantum entropy method (MQEM) is invariant under the arbitrary unitary transformation of the input matrix. Without introducing further ambiguity, Bayesian probabilistic interpretation can be applied to the MQEM. Using our DFT+DMFT package, DMFTpack, the MQEM is applied for real materials, namely Sr₂IrO₄. The application shows that the generalized method provides a reasonable band structure without introducing a material specific base set.

[1] J.-H. Sim and M. J. Han, Phys. Rev. B (in press); arXiv:1804.01683.