Convergence acceleration and stabilization for dynamical-mean-field-theory calculations

TL;DR

This paper demonstrates how mixing techniques from DFT can significantly accelerate and stabilize convergence in DMFT calculations, especially near critical points like the Mott transition, enabling faster and more reliable solutions.

Contribution

It introduces the application of hybridization function mixing and modified Broyden's method to improve convergence and stability in DMFT self-consistency calculations, including unstable and metastable solutions.

Findings

Speed-up factors up to 3 in practical calculations

Effective convergence even near the Mott transition

Ability to obtain unstable and metastable solutions

Abstract

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 (DFT) calculations are also effective in DMFT. As an example, the increase of 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 non-linear self-consistency equation. Speed-up factors as high as 3 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 of the hybridization function, which is related to the propagation of the information between the different energy scales during the iteration.