An Efficient Calculation of the Total Energy Variation in DFT+DMFT Implemented using Orthogonal Basis sets

Calculations of the total energy variation in density functional theory plus dynamical mean field theory (DFT+DMFT) with respect to the structural change are important for atomic force and stress computations for strongly correlated materials. In this talk, we will show that the energy variation of DFT+DMFT implemented using orthogonal basis sets such as Wannier functions can be computed efficiently using analytic formula since the potential energy variation can be exactly cancelled out and the DMFT self-energy itself or its variation does not need to be explicitly accounted. We will use DMFT with the Continuous-Time Quantum Monte Carlo (CTQMC) impurity solver to compute its total energy variation of the two-dimensional one-band Hubbard model with respect to changes of hopping parameters and compare to the results of its analytic energy derivative formula to verify their quantitative agreement. We will also compare the potential energy contributions sampled directly from CTQMC and computed using the Migdal-Galitzki formula. The application of our formula to the calculations of forces and stress in DFT+DMFT will be also discussed.