Convergence acceleration and stabilization of dynamical mean-field theory calculations

The convergence to the self-consistency in the dynamical mean-field theory (DMFT) calculations for models of correlated electron systems can be significantly accelerated by using an appropriate mixing of hybridization functions which are used as the input to the impurity solver. It is shown that the techniques and the past experience with the mixing of input charge densities in the density-functional theory calculations are also effective in DMFT. As an example, the increase in the computational requirements near the Mott metal-insulator transition in the Hubbard model due to critical slowing down can be strongly reduced by using the modified Broyden's method to numerically solve the nonlinear self-consistency equation. Speed-up factors as high as three were observed in practical calculations even for this relatively well-behaved problem. Furthermore, the convergence can be achieved in difficult cases where simple linear mixing is either not effective or even leads to divergence. Unstable and metastable solutions can also be obtained. We also determine the linear response of the system with respect to the variations in the hybridization function, which is related to the propagation of the information between the different energy scales during the iteration.