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

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.

10 pages, 5 figures

References in corpus (19)

• Continuous-time Monte Carlo methods for quantum impurity models
• Quantum Monte Carlo Impurity Solver for Cluster DMFT and Electronic Structure Calculations in Adjustable Base
• Hybridization expansion impurity solver: General formulation and application to Kondo lattice and two-orbital models
• Sum-rule Conserving Spectral Functions from the Numerical Renormalization Group
• Energy resolution and discretization artefacts in the numerical renormalization group
• A Numerical Renormalization Group approach to Green's Functions for Quantum Impurity Models
• Discrete Lehmann representation of imaginary time Green's functions
• Worm Improved Estimators in Continuous-time Quantum Monte Carlo
• Fully Self-Consistent Finite-Temperature $GW$ in Gaussian Bloch Orbitals for Solids
• Robust analytic continuation of Green's functions via projection, pole estimation, and semidefinite relaxation
• libdlr: Efficient imaginary time calculations using the discrete Lehmann representation
• Efficient ab initio many-body calculations based on sparse modeling of Matsubara Green's function
• A fast time domain solver for the equilibrium Dyson equation
• Complex Time Evolution in Tensor Networks
• Sparse modeling of large-scale quantum impurity models with low symmetries
• Superconductivity in the Uniform Electron Gas: Irrelevance of Kohn-Luttinger Mechanism
• Decomposing imaginary time Feynman diagrams using separable basis functions: Anderson impurity model strong coupling expansion
• Low rank Green's function representations applied to dynamical mean-field theory
• Causal optimization method for imaginary-time Green's functions in interacting electron systems

Cited by in corpus (4)

• LiV2O4: Hund-Assisted Orbital-Selective Mottness
• Low-temperature transport in high-conductivity correlated metals: a density-functional plus dynamical mean-field study of cubic perovskites
• Hund flat band in a frustrated spinel oxide
• Automated evaluation of imaginary time strong coupling diagrams by sum-of-exponentials hybridization fitting