Strongly correlated systems of fermions have an interesting phase diagram arising from the Hubbard gap. Excitation across the gap leads to the formation of doubly occupied lattice sites (doublons) which offers interesting electronic and optical properties. Moreover, when the system is driven out of equilibrium interesting collective dynamics may arise that are related to the spatial propagation of doublons. Here, a novel mechanism that was recently proposed by the authors [Balzer et al., Phys. Rev. Lett. 121, 267602 (2018)] is verified by exact diagonalization and nonequilibrium Green functions (NEGF) simulations – fermionic doublon creation by the impact of energetic ions. The formation of a nonequilibrium steady state with homogeneous doublon distribution is reported. The effect should be particularly important for correlated finite systems, such as graphene nanoribbons, and directly observable with fermionic atoms in optical lattices. It is demonstrated that doublon formation and propagation in correlated lattice systems can be accurately simulated with NEGF. In addition to two‐time results, single‐time results within the generalized Kadanoff–Baym ansatz (GKBA) with Hartree–Fock propagators (HF‐GKBA) is presented. Finally systematic improvements of the GKBA that use correlated propagators (correlated GKBA) and a correlated initial state are discussed.
Strongly correlated systems of fermions have an interesting phase diagram arising from the Hubbard gap. Excitation across the gap leads to the formation of doubly occupied lattice sites (doublons) which offers interesting electronic and optical properties. Moreover, when the system is driven out of equilibrium interesting collective dynamics may arise that are related to the spatial propagation of doublons. Here, a novel mechanism that was recently proposed by the authors [Balzer et al., Phys. Rev. Lett. 121, 267602 (2018)] is verified by exact diagonalization and nonequilibrium Green functions (NEGF) simulations – fermionic doublon creation by the impact of energetic ions. The formation of a nonequilibrium steady state with homogeneous doublon distribution is reported. The effect should be particularly important for correlated finite systems, such as graphene nanoribbons, and directly observable with fermionic atoms in optical lattices. It is demonstrated that doublon formation and propagation in correlated lattice systems can be accurately simulated with NEGF. In addition to two‐time results, single‐time results within the generalized Kadanoff–Baym ansatz (GKBA) with Hartree–Fock propagators (HF‐GKBA) is presented. Finally systematic improvements of the GKBA that use correlated propagators (correlated GKBA) and a correlated initial state are discussed.
Strongly correlated systems of fermions have a number of exciting collective properties. Among them, the creation of a lattice that is occupied by doublons, i.e., two quantum particles with opposite spins, offers interesting electronic properties. In the past a variety of methods have been proposed to control doublon formation, both, spatially and temporally. Here, a novel mechanism is proposed and verified by exact diagonalization and nonequilibrium Green functions simulations-fermionic doublon creation by the impact of energetic ions. We report the formation of a nonequilibrium steady state with homogeneous doublon distribution. The effect should be particularly important for strongly correlated finite systems, such as graphene nanoribbons, and directly observable with fermionic atoms in optical lattices.
The Hubbard model is a prototype for strongly correlated many-particle systems, including electrons in condensed matter and molecules, as well as for fermions or bosons in optical lattices. While the equilibrium properties of these systems have been studied in detail, the nonequilibrium dynamics following a strong nonperturbative excitation only recently came into the focus of experiments and theory. It is of particular interest how the dynamics depend on the coupling strength and on the particle number and whether there exist universal features in the time evolution. Here, we present results for the dynamics of finite Hubbard clusters based on a self-consistent nonequilibrium Green functions (NEGF) approach invoking the generalized Kadanoff-Baym ansatz (GKBA). We discuss the conserving properties of the GKBA with Hartree-Fock propagators in detail and present a generalized form of the energy conservation criterion of Baym and Kadanoff for NEGF. Furthermore, we demonstrate that the HF-GKBA cures some artifacts of prior two-time NEGF simulations. Besides, this approach substantially speeds up the numerical calculations and thus presents the capability to study comparatively large systems and to extend the analysis to long times allowing for an accurate computation of the excitation spectrum via time propagation. Our data obtained within the second Born approximation compare favorably with exact diagonalization results (available for up to 13 particles) and are expected to have predictive capability for substantially larger systems in the weak-coupling limit.
The theory of nonequilibrium Green functions (NEGF) has seen a rapid development over the recent three decades. Applications include diverse correlated many‐body systems in and out of equilibrium. Very good agreement with experiments and available exact theoretical results could be demonstrated if the proper selfenergy approximations were used. However, full two‐time NEGF simulations are computationally costly, as they suffer from a cubic scaling of the computation time with the simulation duration. Recently the G1–G2 scheme that exactly reformulates the generalized Kadanoff–Baym ansatz with Hartree–Fock propagators (HF‐GKBA) into time‐local equations is introduced, which achieves time‐linear scaling and allows for a dramatic speedup and extension of the simulations (Schluenzen et al. Phys. Rev. Lett. 2020, 124, 076601). Remarkably, this scaling is achieved quickly, and also for high‐level selfenergies, including the nonequilibrium GW and T‐matrix approximations (Joost et al. Phys. Rev. B 2020, 101, 245101). Even the dynamically screened ladder approximation is now feasible (Joost et al. Phys. Rev. B 2022, 105, 165155), and also applications to electron‐boson systems are demonstrated. Herein, an overview on recent results that are achieved with the G1–G2 scheme is presented. Problems and open questions are discussed and further ideas of how to overcome the current limitations of the scheme and present are presented. The G1–G2 scheme is illustrated by presenting applying it to the excitation dynamics of Hubbard clusters, to optical excitation of graphene, and to charge transfer during stopping of ions by correlated materials.
The nonequilibrium Green's functions (NEGF) method has proven to be a powerful tool to describe quantum behavior for a variety of correlated many-body systems out of equilibrium. The cover image shows results of NEGF calculations of the response of a correlated chain of electrons in a Hubbard lattice to the impact of charged particles. The ions produce a local increase of the double occupation at the impact point, that is spreading through the system. With each successive particle impact the double-occupation level is significantly increased in time and gives rise to stable, delocalized doublons–bound electron pairs. For more details see article no. 1800490 by Michael Bonitz et al. within the special section “Non-Equilibrium Green's Functions”, guest-edited by Gianluca Stefanucci, Andrea Marini, and Stefano Bellucci (cf. also the Preface, article no. 1900335).
This article presents an overview on recent progress in the theory of nonequilibrium Green functions (NEGF). We discuss applications of NEGF simulations to describe the femtosecond dynamics of various finite fermionic systems following an excitation out of equilibrium. This includes the expansion dynamics of ultracold atoms in optical lattices following a confinement quench and the excitation of strongly correlated electrons in a solid by the impact of a charged particle. NEGF, presently, are the only ab initio quantum approach that is able to study the dynamics of correlations for long times in two and three dimensions. However, until recently, NEGF simulations have mostly been performed with rather simple selfenergy approximations such as the second-order Born approximation (SOA). While they correctly capture the qualitative trends of the relaxation towards equilibrium, the reliability and accuracy of these NEGF simulations has remained open, for a long time. Here we report on recent tests of NEGF simulations for finite lattice systems against exact-diagonalization and density-matrix-renormalization-group benchmark data. The results confirm the high accuracy and predictive capability of NEGF simulations-provided selfenergies are used that go beyond the SOA and adequately include strong correlation and dynamical-screening effects. With an extended arsenal of selfenergies that can be used effectively, the NEGF approach has the potential of becoming a powerful simulation tool with broad areas of new applications including strongly correlated solids and ultracold atoms. The present review aims at making such applications possible. To this end we present a selfcontained introduction to the theory of NEGF and give an overview on recent numerical applications to compute the ultrafast relaxation dynamics of correlated fermions. In the second part we give a detailed introduction to selfenergies beyond the SOA. Important examples are the third-order approximation, the [Formula: see text] approximation, the T-matrix approximation and the fluctuating-exchange approximation. We give a comprehensive summary of the explicit selfenergy expressions for a variety of systems of practical relevance, starting from the most general expressions (general basis) and the Feynman diagrams, and including also the important cases of diagonal basis sets, the Hubbard model and the differences occuring for bosons and fermions. With these details, and information on the computational effort and scaling with the basis size and propagation duration, readers will be able to choose the proper basis set and straightforwardly implement and apply advanced selfenergy approximations to a broad class of systems.