Time-resolved photoemission spectroscopy provides a unique and direct way to explore the real-time nonequilibrium dynamics of electrons and holes. The formal theory of the spectral function evolution requires inclusion of electronic correlations and dissipation, which are challenging due to the associated long simulation timescales which translate to a high computational cost. Recent methodological developments, namely the Real-Time Dyson Expansion, as well as theoretical developments of many-body perturbation theory for dissipative systems, have allowed for the study of driven-dissipative interacting quantum systems. In this work, we implement the hitherto unrealized study of driven-dissipative interacting quantum systems which includes driven dynamical correlations and utilizes these new methods and perturbative expansions. We illustrate the combined formalism on a prototypical two-band semiconductor model with long-range density-density Coulomb interactions. We show that the intraband thermalization of conduction band electrons induces nontrivial time-dependent changes in the system's bandstructure and a time-evolving band-gap renormalization (with a reduction by up to 10\%). We show that the qualitative features are preserved for a variety of parameters, discuss the corresponding spectral dynamics, and provide an outlook on the newly introduced simulation framework, which enables treating electron-electron scattering and dissipation effects on equal footing.
Time-resolved photoemission spectroscopy provides a unique and direct way to explore the real-time nonequilibrium dynamics of electrons and holes. The formal theory of the spectral function evolution requires inclusion of electronic correlations and dissipation, which are challenging due to the associated long simulation timescales which translate to a high computational cost. Recent methodological developments, namely the Real-Time Dyson Expansion, as well as theoretical developments of many-body perturbation theory for dissipative systems, have allowed for the study of driven-dissipative interacting quantum systems. In this work, we implement the hitherto unrealized study of driven-dissipative interacting quantum systems which includes driven dynamical correlations and utilizes these new methods and perturbative expansions. We illustrate the combined formalism on a prototypical two-band semiconductor model with long-range density-density Coulomb interactions. We show that the intraband thermalization of conduction band electrons induces nontrivial time-dependent changes in the system's bandstructure and a time-evolving band-gap renormalization (with a reduction by up to 10%). We show that the qualitative features are preserved for a variety of parameters, discuss the corresponding spectral dynamics, and provide an outlook on the newly introduced simulation framework, which enables treating electron-electron scattering and dissipation effects on equal footing.
Time-resolved photoemission spectroscopy provides a unique and direct way to explore the real-time nonequilibrium dynamics of electrons and holes. The formal theory of spectral function evolution requires inclusion of electronic correlations and dissipation, which are challenging due to the associated long simulation timescales which translate to a high computational cost. Recent methodological developments, namely, the real-time Dyson expansion, as well as theoretical developments of many-body perturbation theory for dissipative systems, have allowed for the study of driven-dissipative interacting quantum systems. In this work, we implement the hitherto unrealized study of driven dynamically correlated systems and utilize these methods and perturbative expansions. We illustrate the combined formalism on a prototypical two-band semiconductor model with long-range density-density Coulomb interactions. We show that the intraband thermalization of conduction band electrons induces nontrivial time-dependent changes in the system's band structure and a time-evolving band-gap renormalization (with a reduction by up to 8.4%). We show that the qualitative features are preserved for a variety of parameters, discuss the corresponding spectral dynamics, and provide an outlook on the introduced simulation framework, which enables treating electron-electron scattering and dissipation effects on equal footing.
Time-resolved photoemission spectroscopy is the key technique to probe the real-time nonequilibrium dynamics of electronic states. Theoretical predictions of the time dependent spectral function for realistic systems is however, a challenge. Employing the Kadanoff-Baym equations to find this quantity results in a cubic scaling in the total number of time steps, quickly becoming prohibitive and often fail quantitatively and even qualitatively. In comparison, mean-field methods have more favorable numerical scaling both in the number of time steps and in the complexity associated with the cost of evolving for a single time step, however they miss key spectral properties such as emergent spectral features. Here we present a scheme that allows for the inclusion of dynamical correlations to the spectral function while maintaining the same scaling in the number of time steps as for mean-field approaches, while capturing the emergent physics. Further, the scheme can be efficiently implemented on top of equilibrium real-time many-body perturbation theory schemes and codes. We see excellent agreement with exact results for test systems. Furthermore, we exemplify the method on a periodic system and demonstrate clear evidence that our proposed scheme produces complex spectral features including excitonic band replicas, features that are not observed using static mean-field approaches.
We present a systematic comparison of the real-time Dyson expansion (RTDE) with established non-equilibrium Green's function approaches for simulating driven, interacting quantum systems. Focusing on density matrix dynamics, time-off-diagonal Green's functions, and time-resolved photoemission spectra, we benchmark RTDE against fully self-consistent Kadanoff-Baym equation (KBE) calculations, the generalized Kadanoff-Baym ansatz (GKBA), and exact diagonalization for small systems using second order many-body perturbation theory. Using a driven two-band Hubbard model, we show that mean-field single particle density matrix trajectories provide a reliable baseline for RTDE across a broad range of interaction strengths and excited-carrier populations. Further, RTDE accurately captures correlation effects in the Green's functions, including long-lived oscillations and revivals that are strongly suppressed by the overdamping inherent to self-consistent KBE schemes. As a consequence, RTDE resolves rich non-equilibrium spectral structure in time-resolved photoemission, such as interaction- and population-dependent quasiparticle splittings and bandgap renormalization, which are largely washed out in self-consistent approaches, yet are present in the exact solutions. Our results demonstrate that RTDE bridges the gap between mean-field propagation and full two-time KBE simulations, retaining favorable linear scaling while capturing essential dynamical correlations relevant for ultrafast spectroscopy.
Time-resolved spectroscopy is a powerful tool for probing electron dynamics in molecules and solids, revealing transient phenomena on subfemtosecond time scales. The interpretation of experimental results is often enhanced by parallel numerical studies, which can provide insight and validation for experimental hypotheses. However, developing a theoretical framework for simulating time-resolved spectra remains a significant challenge. The most suitable approach involves the many-body nonequilibrium Green’s function formalism, which accounts for crucial dynamical many-body correlations during time evolution. While these dynamical correlations are essential for observing emergent behavior in time-resolved spectra, they also render the formalism prohibitively expensive for large-scale simulations. Substantial effort has been devoted to reducing this computational cost─through approximations and numerical techniques─while preserving the key dynamical correlations. The ultimate goal is to enable first-principles simulations of time-dependent systems ranging from small molecules to large, periodic, multidimensional solids. In this perspective, we outline key challenges in developing practical simulations for time-resolved spectroscopy, with a particular focus on Green’s function methodologies. We highlight a recent advancement toward a scalable framework: the real-time Dyson expansion (RT-DE) [ Phys. Rev. Lett. 2024, 133, 226902]. We introduce the theoretical foundation of RT-DE and discuss strategies for improving scalability, which have already enabled simulations of system sizes beyond the reach of previous fully dynamical approaches. We conclude with an outlook on future directions for extending RT-DE to first-principles studies of dynamically correlated, nonequilibrium systems.
Time-resolved photoemission spectroscopy is the key technique to probe the real-time non-equilibrium dynamics of electronic states. Theoretical predictions of the time dependent spectral function for realistic systems is however, a challenge. Employing the Kadanoff-Baym equations to find this quantity results in a cubic scaling in the total number of time steps, quickly becoming prohibitive and often fail quantitatively and even qualitatively. In comparison, mean-field methods have more favorable numerical scaling both in the number of time steps and in the complexity associated with the cost of evolving for a single time step, however they miss key spectral properties such as emergent spectral features. Here we present a scheme that allows for the inclusion of dynamical correlations to the spectral function while maintaining the same scaling in the number of time steps as for mean-field approaches, while capturing the emergent physics. Further, the scheme can be efficiently implemented on top of equilibrium real-time many-body perturbation theory schemes and codes. We see excellent agreement with exact results for test systems. Furthermore we exemplify the method on a periodic system and demonstrate clear evidence that our proposed scheme produces complex spectral features including excitonic band replicas, features that are not observed using static mean-field approaches.
The problem of quantum dynamics in open systems has gained attention in recent decades and not the least due to the advances made in quantum transport in molecular systems. The main motivation behind quantum transport and molecular electronics is the futuristic goal to be able at some point to replace, or to complement, the silicon-based technology and to make the electronic devices faster. On a fundamental level, one has to deal with time-dependent processes where electron-electron or electron- phonon interactions are of great importance, and they can cause profound quantitative and qualitative changes on the physical and dynamical properties of electronic systems compared to the non-interacting case. Most of the studies of quantum transport have been focused on the steady-state description while neglecting the short-time dynamics. However, the dynamical effects are of great importance since fast- switching processes play a pivotal role in the operation of future devices. We studied the problem of time-dependent electron transport through the Anderson impurity model by using many-body perturbation theory (MBPT) together with Keldysh Green’s functions as well as with time-dependent density functional theory (TDDFT). These methods were compared with numerically exact time-dependent density-matrix renormalization group (tDMRG) method. We found that the many-body perturbation theory results beyond Hartree-Fock approximation were in close agreement with tDMRG results. In addition we studied the possibility of multistablity in the density and current of an interacting nanoscale junction as well as how to reversibly switch between the multiple solutions in time domain. An accurate theoretical treatment of electron correlation even in as simple model as an interacting electron gas at metallic densities still continues to be a challenge; especially description of features in the photoemission spectra due to electron correlations provides a theoretical challenge. The many-body perturbation theory yields a systematic way to study electron-electron (electron-phonon) correlations in various systems. One of the widely used approximations in MBPT is the GW approximation in which the bare interaction line is replaced with screened interaction line in the first order exchange diagram. The GW approximation gives good estimates for the band gap values close to experimental ones but especially the self-consistent GW approximation has a number of deficiencies like washing out of plasmon features and overestimation of bandwidths compared to experiment. One way to improve GW calculations is to include vertex corrections. Unfortunately, the straightforward inclusion of vertex corrections yields negative spectra in some frequency regions. We developed a diagrammatic approach to construct self-energy approximations with positive spectral properties. Our approach consists of expressing a self-energy of response diagram as a product of half-diagrams after which a minimal set of additional diagrams is identified to construct a perfect square. We applied this method to study vertex corrections in a homogeneous electron gas. In addition we analyzed the diagrammatic content of photocurrent with density functional theory. The expression for the photocurrent was obtained as an integral over the Kohn-Sham spectral function renormalized by effective potentials that depend on the exchange correlation kernel of current density functional theory. The expression for the photocurrent gives us the angular dependence of the photocurrent but it does not provide a direct access to the kinetic energy distribution of the photoelectrons.