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

Abstract

We propose a description of nonequilibrium systems via a simple protocol that combines exchangecorrelation 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 Hubbardtype 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. DOI: 10.1103/PhysRevLett.116.236402 Hybrid methods are a valuable option in physics, to merge concepts and perspectives into a more general and effective level of description. This Letter adds an item from condensed matter physics to the list; we propose a hybrid method that combines nonperturbative exchangecorrelation (XC) potentials from time dependent density functional theory (TDDFT) [1-3] with many-body perturbative self-energy schemes from nonequilibrium Green's functions (NEGF) [4][5][6][7], to deal with systems with strong electronic correlations and out of equilibrium.An accurate first-principles description of the real-time dynamics of systems with strong electronic correlations is an important, difficult, and basically unsolved problem of condensed matter research. General frameworks like TDDFT and NEGF do indeed allow for an in-principleexact treatment of strong electronic correlations. However, they both rely on key ingredients (the XC potential for TDDFT and the self-energy Σ for the NEGF) that in general are only approximately known. For TDDFT, a systematic and general way to include nonlocal, nonadiabatic effects in the XC potential is lacking, while for NEGF a main hindrance is that self-energies based on many-body perturbation theory, already computationally demanding, are usually inadequate for strong electronic correlations. While considerable progress has been made for model systems far away from equilibrium (see, e.g., [8][9][10][11][12][13][14]) or for the ab initio description of nearequilibrium situations (see, e.g., [15,16]), a reliable firstprinciples treatment of the far-from-equilibrium regime is still lacking.Here, we suggest a step towards the solution of this problem, by a novel combination of TDDFT and NEGF, where perturbative (but systematic) memory-effect corrections augment a nonperturbative local adiabatic treatment of electronic correlations. The approach is fully conserving in the Kadanoff-Baym sense [17] and, using the so-called generalized Kadanoff-Baym ansatz [18] (see below), can be made viable for realistic systems.Putting in practice our proposal at the ab initio level requires access to continuum nonperturbative XC potentials, and this point is addressed at the end of the paper. However, the scope of our method can already be illustrated here using simple lattice models. This has th...

Hypergeometric resummation of self-consistent sunset diagrams for steady-state electron-boson quantum many-body systems out of equilibrium

“…Also, very recent studies have shown that self-consistent Φ-derivable approximations can converge to unphysical solutions; [34][35][36][37][38][39][40][41][42][43][44]47,48 similar issues have been noted in the context of time-dependent simulations [40][41][42][43][44][47][48][49] using the Kadanoff-Baym equations, but can be remedied by introducing self-consistent contributions in controlled fashion. 43 Nevertheless, the use of self-consistent MBPT may be justified to some extent.…”

“…Timedependent problems are typically approached by means of self-consistent Φ-derivable self-energy approximations within the Keldysh-Kadanoff-Baym equations (KBE). Great progress has been made recently towards the appli- cation of KBE to realistic stationary and time-dependent systems, [40][41][42][43][44]47,48 . Interestingly, for very small systems under strong driving fields, unphysical behaviour of self-consistent solutions from Φ-derivable approximations have been also reported in this context.…”

Exchange-Correlation Energy Densities and Response Potentials: Connection Between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond

“…We have identified a fundamental difference between two definitions of the XC energy In addition, we have proposed a working model for the XC and response potential in the strong-coupling limit of DFT for a two-electron stretched dimer, which is very accurate in the dissociation limit. Although restrictied to the 1D case, it could prove useful, e.g., to model quantum transport calculations 55 and systems out of equilibrium in hybrid approaches, 64 but also as a starting point to build new approximations that would also include the missing kinetic correlation component.…”

A v0-representability issue in lattice ensemble-DFT and its signature in lattice TDDFT

“…Thus the interaction term only appears in the total-symmetric block (IRREP A 1 ), i.e. in the 3-cluster [26,73,74].…”