Real-frequency quantum field theory applied to the single-impurity Anderson model

Abstract

A major challenge in the field of correlated electrons is the computation of dynamical correlation functions. For comparisons with experiment, one is interested in their real-frequency dependence. This is difficult to compute, as imaginary-frequency data from the Matsubara formalism require analytic continuation, a numerically ill-posed problem. Here, we apply quantum field theory to the single-impurity Anderson model (AM), using the Keldysh instead of the Matsubara formalism with direct access to the self-energy and dynamical susceptibilities on the real-frequency axis. We present results from the functional renormalization group (fRG) at one-loop level and from solving the self-consistent parquet equations in the parquet approximation. In contrast to previous Keldysh fRG works, we employ a parametrization of the four-point vertex which captures its full dependence on three real-frequency arguments. We compare our results to benchmark data obtained with the numerical renormalization group and to second-order perturbation theory. We find that capturing the full frequency dependence of the four-point vertex significantly improves the fRG results compared to previous implementations, and that solving the parquet equations yields the best agreement with the NRG benchmark data, but is only feasible up to moderate interaction strengths. Our methodical advances pave the way for treating more complicated models in the future.

26 pages, 21 figures

References in corpus (11)

• The numerical renormalization group method for quantum impurity systems
• Dynamical vertex approximation - a step beyond dynamical mean field theory
• 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
• Non-existence of the Luttinger-Ward functional and misleading convergence of skeleton diagrammatic series for Hubbard-like models
• A finite-frequency functional RG approach to the single impurity Anderson model
• Field dependent quasiparticles in the infinite dimensional Hubbard model
• Algorithmic approach to diagrammatic expansions for real-frequency evaluation of susceptibility functions
• Quantum Quasi-Monte Carlo algorithm for out-of-equilibrium Green functions at long times
• Ward identities for the Anderson impurity model: derivation via functional methods and the exact renormalization group

Cited by in corpus (13)

• Pseudo-fermion functional renormalization group for spin models
• Symmetric improved estimators for multipoint vertex functions
• KeldyshQFT: A C++ codebase for real-frequency multiloop functional renormalization group and parquet computations of the single-impurity Anderson model
• Analytic continuation of multipoint correlation functions
• Testing the parquet equations and the U(1) Ward identity for real-frequency correlation functions from the multipoint numerical renormalization group
• Subleading logarithmic behavior in the parquet formalism
• The finite-difference parquet method: Enhanced electron-paramagnon scattering opens a pseudogap
• Keldysh pseudo-fermion functional renormalization group for quantum magnetism
• Compressing local vertex functions from the multipoint numerical renormalization group using quantics tensor cross interpolation
• Kondo spectral functions at low-temperatures: A dynamical-exchange-correlation-field perspective
• Improvement of the simplification method for the local two-particle full-vertex towards precise frequency behavior
• Functional renormalization with interaction flows: A single-boson exchange perspective and application to electron-phonon systems
• Many-body correlations in Floquet steady-states: Frequency-resolved renormalization group of the driven Anderson impurity