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

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.

9 pages, 8 figures

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• Extremely correlated Fermi liquid theory meets Dynamical mean-field theory: Analytical insights into the doping-driven Mott transition
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• Nonequilibrium diagrammatic many-body simulations with quantics tensor trains
• Repulsive vs. attractive Hubbard model: transport properties and spin-lattice relaxation rate
• A Strange Metal from Gutzwiller correlations in infinite dimensions
• Kinks in the periodic Anderson model
• Cluster Extended Dynamical Mean Field Approach and Unconventional Superconductivity
• Fine structure of spectra in the antiferromagnetic phase of the Kondo lattice model
• Entropy and specific heat of the infinite-dimensional three-orbital Hubbard model
• Quantum criticality in the spin-isotropic pseudogap Bose-Fermi Kondo model: entropy, scaling, and the g-theorem
• Suppression of the Mott insulating phase in the particle-hole asymmetric Hubbard model
• Universal Mott quantum criticality in a modified periodic Anderson model