Accelerating dynamical mean-field theory convergence by preconditioning with computationally cheaper quantum embedding methods

TL;DR

This paper demonstrates that initializing dynamical mean-field theory (DMFT) with solutions from cheaper quantum embedding methods significantly accelerates convergence, especially near the Mott transition, reducing computational costs and improving reliability.

Contribution

The study introduces a novel approach of using quantum embedding methods like RISB and g-RISB for DMFT initialization to enhance convergence speed and stability.

Findings

g-RISB initialization reduces DMFT iterations by up to tenfold.

Single iteration after g-RISB initialization often recovers full dynamical structure.

The method is particularly effective near the Mott transition.

Abstract

Dynamical mean-field theory (DMFT) is a cornerstone technique for studying strongly correlated electronic systems. However, each DMFT step is computationally demanding, and many iterations can be required to achieve convergence. Here, we accelerate the convergence of DMFT by initializing its self-consistent cycle with solutions from computationally cheaper and more approximate methods. We compare the initialization with the non-interacting solution to a range of quantum embedding compatible approaches: Hartree-Fock, the Hubbard-I approximation, rotationally invariant slave bosons (RISB), and its ghost extension (g-RISB). We find that these initializations can reduce the number of DMFT iterations by up to an order of magnitude, with g-RISB providing the most effective and reliable benefits. In most regimes, initializing with g-RISB and performing a single DMFT iteration suffices to recover the full dynamical structure. The improvement in convergence is controlled by the initial solution's accuracy in the low-energy part of the self-energy, on the scale of the non-interacting bandwidth. This strategy is especially effective at the Mott insulator-metal transition, where an initialization from the non-interacting limit can lead to a breakdown of DMFT due to the sign problem. Our results establish the usage of accurate yet cheaper quantum embedding methods as a powerful means to substantially reduce the computational cost of DMFT, particularly in regimes where convergence is slow or prone to failure.