DFT + Embedded DMFT Functional Overview

• [1] Electronic structure calculations with dynamical mean-field theory, G. Kotliar, S. Y. Savrasov, K. Haule, et.al., Rev. Mod. Phys. 78, 865 (2006).
• [2] Dynamical mean-field theory within the full-potential methods, K. Haule, C.-H. Yee, and K. Kim, Phys. Rev. B 81, 195107 (2010).
• [3] Exact double-counting in combining the Dynamical Mean Field Theory and the Density Functional Theory, K. Haule, PRL 115, 196403 (2015).
• [4] Quantum Monte Carlo Impurity Solver for Cluster DMFT and Electronic Structure Calculations, Kristjan Haule, Phys. Rev. B 75, 155113 (2007).
• [5] Free energy from stationary implementation of the DFT+DMFT functional, K. Haule and T. Birol, PRL 115, 256402 (2015).
• [6] Forces for Structural Optimizations in Correlated Materials within DFT+Embedded DMFT Functional Approach, K. Haule, G. L. Pascut, arXiv:1602.02819.

The Density Functional Theory implementation within Wien2k consists of several steps (see wien2k-documentation) depicted in the Figure:

The steps are:

• lapw0: calculates electronic potential
• lapw1: solves eigenvalue problem for Kohn-Sham orbitals
• lapwso: adds spin-orbit coupling
• lapw2: calculates DFT valence electronic charge
• core: adds core states to DFT charge
• mixer: mixes electronic charge density

The DMFT+DMFT inserts two new steps (dmft1 and impurity solver) and replaces lapw2 with dmft2 step. The process looks like that:

The eDMFT steps are:

• lapw0: calculates electronic potential
• lapw1: solves eigenvalue problem for Kohn-Sham orbitals
• lapwso: adds spin-orbit coupling
• dmft1: calculates local green's function and hybridization function
• impurity: solves the auxiliary impurity problem for electronic self-energy correction
• dmft2: calculates DMFT+DFT valence electronic charge
• core: adds core states to DFT charge
• mixer: mixes electronic charge density

The eDMFT can be broaken into two loops: the DFT loop (grey area in Figure above) and the DMFT loop (red area in Figure above). We can repeat several times the DMFT loop to better converge the DMFT self-energy computed by the impurity solver (this part is so-called non-charge self-consistent DMFT). The DFT charge loop can also be iterated several times using fixed self-energy to better converge electronic charge.

The number of DFT steps and DMFT steps can be controled by the input file "params.dat". The fastest convergence is usually achieved by requiring that roughly the same amount of time is spend in both steps.

There are three main steps in eDMFT calculation,

• Impurity solver: Can be CTQMC, OCA, NCA.
• dmft1 step : calculates the local green's function and hybridization
• dmft2 step : calculated electronic charge and free energy

More details of dmft1 and dmft2 steps are shown below: