Stabilizing the calculation of the self-energy in dynamical mean-field theory using constrained residual minimization

TL;DR

This paper introduces a new constrained residual minimization method to stabilize self-energy calculations in dynamical mean-field theory, improving numerical stability and efficiency in solving the Dyson equation.

Contribution

The paper presents a novel optimization-based approach that incorporates asymptotic expansion constraints and the Lehmann representation to enhance self-energy computation in DMFT.

Findings

Reduces numerical instability in self-energy calculations.

Efficiently handles both model and ab-initio systems.

Demonstrates improved accuracy in benchmark tests.

Abstract

We propose a simple and efficient method to calculate the electronic self-energy in dynamical mean-field theory (DMFT), addressing a numerical instability often encountered when solving the Dyson equation. Our approach formulates the Dyson equation as a constrained optimization problem with a simple quadratic objective. The constraints on the self-energy are obtained via direct measurement of the leading order terms of its asymptotic expansion within a continuous time quantum Monte Carlo framework, and the use of the compact discrete Lehmann representation of the self-energy yields an optimization problem in a modest number of unknowns. We benchmark our method for the non-interacting Bethe lattice, as well as DMFT calculations for both model systems and ab-initio applications.