Partial self-consistency and analyticity in many-body perturbation theory: Particle number conservation and a generalized sum rule

We consider a general class of approximations which guarantees the conservation of particle number in many-body perturbation theory. To do this we extend the concept of $\Phi$-derivability for the self-energy $\Sigma$ to a larger class of diagrammatic terms in which only some of the Green's function lines contain the fully dressed Green's function $G$. We call the corresponding approximations for $\Sigma$ partially $\Phi$-derivable. A special subclass of such approximations, which are gauge-invariant, is obtained by dressing loops in the diagrammatic expansion of $\Phi$ consistently with $G$. These approximations are number conserving but do not have to fulfill other conservation laws, such…

Merging Features from Green's Functions and Time Dependent Density Functional Theory: A Route to the Description of Correlated Materials out of Equilibrium?

We propose a description of nonequilibrium systems via a simple protocol that combines exchange-correlation potentials from density functional theory with self-energies of many-body perturbation theory. The approach, aimed to avoid double counting of interactions, is tested against exact results in Hubbard-type systems, with respect to interaction strength, perturbation speed and inhomogeneity, and system dimensionality and size. In many regimes, we find significant improvement over adiabatic time dependent density functional theory or second Born nonequilibrium Green's function approximations. We briefly discuss the reasons for the residual discrepancies, and directions for future work.

Time-linear scaling nonequilibrium Green's function methods for real-time simulations of interacting electrons and bosons. I : Formalism

Simulations of interacting electrons and bosons out of equilibrium, starting from first principles and aiming at realistic multiscale scenarios, is a grand theoretical challenge. Here, using the formalism of nonequilibrium Green's functions and relying in a crucial way on the recently discovered time-linear formulation of the Kadanoff-Baym equations, we present a versatile toolbox for the simulation of correlated electron-boson dynamics. A large class of methods are available, from the Ehrenfest to the dressed GD for the treatment of electron-boson interactions in combination with perturbative, i.e., Hartree-Fock and second-Born, or nonperturbative, i.e., GW and T matrices either without or…

Diagrammatic Expansion for Positive Spectral Functions in the Steady-State Limit

Recently, a method was presented for constructing self-energies within many-body perturbation theory that are guaranteed to produce a positive spectral function for equilibrium systems, by representing the self-energy as a product of half-diagrams on the forward and backward branches of the Keldysh contour. We derive an alternative half-diagram representation that is based on products of retarded diagrams. Our approach extends the method to systems out of equilibrium. When a steady-state limit exists, we show that our approach yields a positive definite spectral function in the frequency domain.

Phononic heat transport in the transient regime: An analytic solution

We investigate the time-resolved quantum transport properties of phonons in arbitrary harmonic systems connected to phonon baths at different temperatures. We obtain a closed analytic expression of the time-dependent one-particle reduced density matrix by explicitly solving the equations of motion for the nonequilibrium Green's function. This is achieved through a well-controlled approximation of the frequency-dependent bath self-energy. Our result allows for exploring transient oscillations and relaxation times of local heat currents, and correctly reduces to an earlier known result in the steady-state limit. We apply the formalism to atomic chains, and benchmark the validity of the approx…

Cutting rules and positivity in finite temperature many-body theory

Abstract For a given diagrammatic approximation in many-body perturbation theory it is not guaranteed that positive observables, such as the density or the spectral function, retain their positivity. For zero-temperature systems we developed a method [2014 Phys. Rev. B 90 115134] based on so-called cutting rules for Feynman diagrams that enforces these properties diagrammatically, thus solving the problem of negative spectral densities observed for various vertex approximations. In this work we extend this method to systems at finite temperature by formulating the cutting rules in terms of retarded N-point functions, thereby simplifying earlier approaches and simultaneously solving the issu…

The generalized Kadanoff-Baym ansatz with initial correlations

Within the non-equilibrium Green's function (NEGF) formalism, the Generalized Kadanoff-Baym Ansatz (GKBA) has stood out as a computationally cheap method to investigate the dynamics of interacting quantum systems driven out of equilibrium. Current implementations of the NEGF--GKBA, however, suffer from a drawback: real-time simulations require {\em noncorrelated} states as initial states. Consequently, initial correlations must be built up through an adiabatic switching of the interaction before turning on any external field, a procedure that can be numerically highly expensive. In this work, we extend the NEGF--GKBA to allow for {\em correlated} states as initial states. Our scheme makes i…

Time-dependent density-functional theory for strongly interacting electrons

We consider an analytically solvable model of two interacting electrons that allows for the calculation of the exact exchange-correlation kernel of time-dependent density functional theory. This kernel, as well as the corresponding density response function, is studied in the limit of large repulsive interactions between the electrons and we give analytical results for these quantities as an asymptotic expansion in powers of the square root of the interaction strength. We find that in the strong interaction limit the three leading terms in the expansion of the kernel act instantaneously while memory terms only appear in the next orders. We further derive an alternative expansion for the ker…

Contour calculus for many-particle functions

In non-equilibrium many-body perturbation theory, Langreth rules are an efficient way to extract real-time equations from contour ones. However, the standard rules are not applicable in cases that do not reduce to simple convolutions and multiplications. We introduce a procedure for extracting real-time equations from general multi-argument contour functions with an arbitrary number of arguments. This is done for both the standard Keldysh contour, as well as the extended contour with a vertical track that allows for general initial states. This amounts to the generalization of the standard Langreth rules to much more general situations. These rules involve multi-argument retarded functions …

Disorder and interactions in systems out of equilibrium : the exact independent-particle picture from density functional theory

Density functional theory (DFT) exploits an independent-particle-system construction to replicate the densities and current of an interacting system. This construction is used here to access the exact effective potential and bias of non-equilibrium systems with disorder and interactions. Our results show that interactions smoothen the effective disorder landscape, but do not necessarily increase the current, due to the competition of disorder screening and effective bias. This puts forward DFT as a diagnostic tool to understand disorder screening in a wide class of interacting disordered systems.

Effective bias and potentials in steady-state quantum transport: A NEGF reverse-engineering study

Using non-equilibrium Green’s functions combined with many-body perturbation theory, we have calculated steady-state densities and currents through short interacting chains subject to a finite electric bias. By using a steady-state reverse-engineering procedure, the effective potential and bias which reproduce such densities and currents in a non-interacting system have been determined. The role of the effective bias is characterised with the aid of the so-called exchange-correlation bias, recently introduced in a steady-state density-functionaltheory formulation for partitioned systems. We find that the effective bias (or, equivalently, the exchange-correlation bias) depends strongly on th…

Time-linear scaling nonequilibrium Green's function method for real-time simulations of interacting electrons and bosons. II : Dynamics of polarons and doublons

Nonequilibrium dynamics of the open chain Holstein-Hubbard model is studied using the linear time-scaling GKBA+ODE scheme developed in Pavlyukh et al. [Phys. Rev. B 105, 125134 (2022)]. We focus on the set of parameters relevant for photovoltaic materials, i.e., a pair of electrons interacting with phonons at the crossover between the adiabatic and antiadiabatic regimes and at moderately large electron-electron interaction. By comparing with exact solutions for two corner cases, we demonstrate the accuracy of the T matrix (in the pp channel) and the second-order Fan (GD) approximations for the treatment of electronic (e−e) and electron-phonon (e-ph) correlations, respectively. The feedback …

Non-equilibrium Green’s Functions for Coupled Fermion-Boson Systems

Fast Green’s Function Method for Ultrafast Electron-Boson Dynamics

The interaction of electrons with quantized phonons and photons underlies the ultrafast dynamics of systems ranging from molecules to solids, and it gives rise to a plethora of physical phenomena experimentally accessible using time-resolved techniques. Green's function methods offer an invaluable interpretation tool since scattering mechanisms of growing complexity can be selectively incorporated in the theory. Currently, however, real-time Green's function simulations are either prohibitively expensive due to the cubic scaling with the propagation time or do neglect the feedback of electrons on the bosons, thus violating energy conservation. We put forward a computationally efficient Gree…