Analytic continuation of multipoint correlation functions

Abstract

Conceptually, the Matsubara formalism (MF), using imaginary frequencies, and the Keldysh formalism (KF), formulated in real frequencies, give equivalent results for systems in thermal equilibrium. The MF has less complexity and is thus more convenient than the KF. However, computing dynamical observables in the MF requires the analytic continuation from imaginary to real frequencies. The analytic continuation is well-known for two-point correlation functions (having one frequency argument), but, for multipoint correlators, a straightforward recipe for deducing all Keldysh components from the MF correlator had not been formulated yet. Recently, a representation of MF and KF correlators in terms of formalism-independent partial spectral functions and formalism-specific kernels was introduced by Kugler, Lee, and von Delft [Phys. Rev. X 11, 041006 (2021)]. We use this representation to formally elucidate the connection between both formalisms. We show how a multipoint MF correlator can be analytically continued to recover all partial spectral functions and yield all Keldysh components of its KF counterpart. The procedure is illustrated for various correlators of the Hubbard atom.

56 pages, 8 figures

References in corpus (43)

• Functional renormalization group approach to correlated fermion systems
• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• Local Electronic Correlation at the Two-Particle Level
• Compressing Green's function using intermediate representation between imaginary-time and real-frequency domains
• Non-existence of the Luttinger-Ward functional and misleading convergence of skeleton diagrammatic series for Hubbard-like models
• Mott physics and spin fluctuations: a unified framework
• A Generalized Fluctuation-Dissipation Theorem for Nonlinear Response Functions
• Nevanlinna Analytical Continuation
• Strong-Coupling Perturbation Theory of the Hubbard Model
• High-frequency asymptotics of the vertex function: diagrammatic parametrization and algorithmic implementation
• Breakdown of traditional many-body theories for correlated electrons
• Non-perturbative landscape of the Mott-Hubbard transition: Multiple divergence lines around the critical endpoint
• Mott physics and spin fluctuations: a functional viewpoint
• Divergences of the irreducible vertex functions in correlated metallic systems: Insights from the Anderson Impurity Model
• Reconstructing the thermal Green functions at real times from those at imaginary times
• Fingerprints of the local moment formation and its Kondo screening in the generalized susceptibilities of many-electron problems
• Analytical Continuation of Matrix-Valued Functions: Carathéodory Formalism
• Discrete Lehmann representation of imaginary time Green's functions
• Practical consequences of Luttinger-Ward functional multivaluedness for cluster DMFT methods
• Single-boson exchange decomposition of the vertex function
• Analytical investigation of singularities in two-particle irreducible vertex functions of the Hubbard atom
• Transmission Probability for Interacting Electrons Connected to Reservoirs
• Superperturbation solver for quantum impurity models
• Algorithmic Matsubara Integration for Hubbard-like models
• Parquet-like equations for the Hedin three-leg vertex
• Robust analytic continuation of Green's functions via projection, pole estimation, and semidefinite relaxation
• Tiling with triangles: parquet and $GW\gamma$ methods unified
• Properties of multi-particle Green and vertex functions within Keldysh formalism
• Fermion-boson vertex within Dynamical Mean-Field Theory
• Solving the Bethe-Salpeter equation with exponential convergence
• Highly nonperturbative nature of the Mott metal-insulator transition: Two-particle vertex divergences in the coexistence region
• Multiloop flow equations for single-boson exchange fRG
• Retarded-Advanced N-point Green Functions in thermal field theories
• Non-perturbative intertwining between spin and charge correlations: A "smoking gun" single-boson-exchange result
• An alternative functional renormalization group approach to the single impurity Anderson model
• On the spectral relations for multitime correlation functions
• Real-frequency quantum field theory applied to the single-impurity Anderson model
• Spectral properties of four-time fermionic Green's functions
• Non-linear responses and three-particle correlators in correlated electron systems exemplified by the Anderson impurity model
• Spectral representation of Matsubara n-point functions: Exact kernel functions and applications
• Symmetric improved estimators for multipoint vertex functions
• Search for Combinations of Thermal n-point Functions with Analytic Extensions
• Keldysh Derivation of Oguri's Linear Conductance Formula for Interacting Fermions

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• KeldyshQFT: A C++ codebase for real-frequency multiloop functional renormalization group and parquet computations of the single-impurity Anderson model
• General Shiba mapping for on-site four-point correlation functions
• Testing the parquet equations and the U(1) Ward identity for real-frequency correlation functions from the multipoint numerical renormalization group
• Overcomplete intermediate representation of two-particle Green's functions and its relation to partial spectral functions
• Imaginary Time Formalism for Causal Nonlinear Response Functions