Abstract: The DFT+DMFT combined with the continuous-time quantum Monte Carlo (CT-QMC) impurity solver is one of the successful approaches to describe correlated electron materials. However, analytic continuation of the QMC data written in the imaginary frequency to the real axis is a difficult numeric problem mainly because of the ill-conditioned kernel matrix. While the maximum entropy method is one of the most suitable choices to gain information from noisy input data, its applications to materials with strong spin-orbit coupling are limited by the non-negative condition of the output spectral function.

In the first part of this talk, I will discuss a newly developed method for the analytic continuation problem, the so-called maximum quantum entropy method (MQEM). It is an extension of the conventional method, introducing quantum relative entropy as a regularization function. The application of the MQEM to a prototype j_eff=1/2 Mott insulator, Sr₂IrO₄, shows that it provides a reasonable band structure without introducing a material-specific basis set. I will also introduce the application of a machine learning technique to the same problem.

In the second part, a simple technique to calculate the branching ratio from a first-principles calculation will be discussed. The calculated ⟨L·S⟩ and branching ratio of different 5d iridates (namely, Sr₂IrO₄, Sr₂MgIrO₆, Sr₂ScIrO₆, and Sr₂TiIrO₆) are in good agreement with recent experimental data. Its reliability and applicability are also carefully examined in the wider material classes.