Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2007.07801 · Physical review. B./Physical review. B

Comparing the generalized Kadanoff-Baym ansatz with the full Kadanoff-Baym equations for an excitonic insulator out of equilibrium

Riku Tuovinen, Denis Golež, Martin Eckstein, Michael A. Sentef

Published Sep 28, 2020• 49 citations
arXivHTMLPDF

Abstract

We investigate out-of-equilibrium dynamics in an excitonic insulator (EI) with a finite-momentum pairing perturbed by a laser-pulse excitation and a sudden coupling to fermionic baths. The transient dynamics of the excitonic order parameter is resolved using the full nonequilibrium Green's function approach and the generalized Kadanoff-Baym ansatz (GKBA) within the second-order Born approximation. The comparison between the two approaches after a laser-pulse excitation shows a good agreement in the weak and the intermediate photodoping regime. In contrast, the laser-pulse dynamics resolved by the GKBA does not show a complete melting of the excitonic order after a strong excitation. Instead we observe persistent oscillations of the excitonic order parameter with a predominant frequency given by the renormalized equilibrium band gap. This anomalous behavior can be overcome within the GKBA formalism by coupling to an external bath, which leads to a transition of the EI system toward the normal state. We analyze the long-time evolution of the system and distinguish decay timescales related to dephasing and thermalization.

DOI
10.1103/physrevb.102.115157

Related papers

Ultrafast nonequilibrium evolution of excitonic modes in semiconductors

Yuta Murakami, Michael Schüler, Shintaro Takayoshi +1 more

We study the time evolution of excitonic states after photoexcitation in the one-dimensional spinless extended Falicov-Kimball model. Several numerical methods are employed and benchmarked against each other: time-dependent mean-field simulations, the second-Born approximation (2BA) within the Kadanoff-Baym formalism, the generalized Kadanoff-Baym ansatz (GKBA) implemented with the 2BA, and the infinite time-evolving block decimation (iTEBD) method. It is found that the GKBA gives the best agreement with iTEBD and captures the relevant physics. Excitations to the particle-hole continuum and resonant excitations of the equilibrium exciton result in a qualitatively different dynamics. In the former case, the exciton binding energy remains positive and the frequency of the corresponding coherent oscillations is smaller than the band gap. On the other hand, resonant excitations trigger a collective mode whose frequency is larger than the band gap. We discuss the origin of these different behaviors by evaluating the nonequilibrium susceptibility using the nonthermal distribution and a random phase approximation. The peculiar mode with frequency larger than the band gap is associated with a partial population inversion with a sharp energy cutoff. We also discuss the effects of the cooling by a phonon bath. We demonstrate the real-time development of coherence in the polarization, which indicates excitonic condensation out of equilibrium.

arXiv:1907.06799•Physical review. B./Physical review. B•Jan 28, 2020•42 citations

Adiabatic Preparation of a Correlated Symmetry-Broken Initial State with the Generalized Kadanoff-Baym Ansatz

Riku Tuovinen, Denis Golež, Michael Schüler +3 more

A fast time propagation method for nonequilibrium Green's functions (NEGF) based on the generalized Kadanoff–Baym Ansatz (GKBA) is applied to a lattice system with a symmetry‐broken equilibrium phase, namely an excitonic insulator (EI). The adiabatic preparation of a correlated symmetry‐broken initial state from a Hartree– Fock wave function within GKBA is assessed by comparing with a solution of the imaginary‐time Dyson equation. It is found that it is possible to reach a symmetry‐ broken correlated initial state with nonzero excitonic order parameter by the adiabatic switching (AS) procedure. It is discussed under which circumstances this is possible in practice within reasonably short switching times.

•Aug 3, 2018•9 citations

Adiabatic Preparation of a Correlated Symmetry‐Broken Initial State with the Generalized Kadanoff–Baym Ansatz

Riku Tuovinen, Denis Golež, Michael Schüler +3 more

A fast time propagation method for nonequilibrium Green's functions (NEGF) based on the generalized Kadanoff–Baym Ansatz (GKBA) is applied to a lattice system with a symmetry‐broken equilibrium phase, namely an excitonic insulator (EI). The adiabatic preparation of a correlated symmetry‐broken initial state from a Hartree–Fock wave function within GKBA is assessed by comparing with a solution of the imaginary‐time Dyson equation. It is found that it is possible to reach a symmetry‐broken correlated initial state with nonzero excitonic order parameter by the adiabatic switching (AS) procedure. It is discussed under which circumstances this is possible in practice within reasonably short switching times.

arXiv:1808.00712•physica status solidi (b)•Dec 3, 2018•23 citations

Hubbard nanoclusters far from equilibrium

S. Hermanns, Niclas Schlünzen, M. Bönitz

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.

arXiv:1402.7300•Physical Review B•Sep 5, 2014•80 citations

Quenching the Hubbard Model: Comparison of Nonequilibrium Green's Function Methods

Jan‐Philip Joost, Christopher Makait, Alexander Osterkorn +1 more

ABSTRACT We benchmark nonequilibrium Green's function (NEGF) approaches for interaction quenches in the half‐filled Fermi–Hubbard model in one and two dimensions. We compare fully self‐consistent two‐time Kadanoff–Baym equations (KBE), the generalized Kadanoff–Baym ansatz (GKBA), and the recently developed NEGF‐based quantum fluctuations approach (NEGF‐QF) with second‐order Born (2B) and GW self‐energies. As references, we use DMRG in 1D and time‐dependent perturbation theory at weak coupling. While all methods reproduce the early‐time build‐up of correlations (prethermalization), different deficiencies emerge during the slower relaxation in the long‐time limit: KBE shows overdamped oscillations, GKBA exhibits a negative overshoot of the Fermi‐surface jump, and NEGF‐QF develops a prethermalization plateau with delayed relaxation. In 1D, we find that GKBA + 2B agrees best with DMRG across the explored parameter range, while QF + GW deviates the most, consistent with its reduced self‐consistency. In 2D, all approaches correctly capture the momentum‐dependence of the relaxation dynamics.

Contributions to Plasma Physics•Jan 15, 2026•1 citation

The generalized Kadanoff-Baym ansatz with initial correlations

Daniel Karlsson, Robert van Leeuwen, Enrico Perfetto +1 more

Within the nonequilibrium 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 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 correlated states as initial states. Our scheme makes it possible to efficiently separate the calculation of the initial state from the real-time simulation, thus paving the way for enlarging the class of systems and external drivings accessible by the already successful NEGF-GKBA. We demonstrate the accuracy of the method and its improved performance in a model donor-acceptor dyad driven out of equilibrium by an external laser pulse.

arXiv:1806.05639•Physical review. B./Physical review. B•Sep 25, 2018•37 citations
We investigate out-of-equilibrium dynamics in an excitonic insulator (EI) with a finite-momentum pairing perturbed by a laser-pulse excitation and a sudden coupling to fermionic baths. The transient dynamics of the excitonic order parameter is resolved using the full nonequilibrium Green's function approach and the generalized Kadanoff-Baym ansatz (GKBA) within the second-order Born approximation. The comparison between the two approaches after a laser-pulse excitation shows a good agreement in the weak and the intermediate photodoping regime. In contrast, the laser-pulse dynamics resolved by the GKBA does not show a complete melting of the excitonic order after a strong excitation. Instead we observe persistent oscillations of the excitonic order parameter with a predominant frequency given by the renormalized equilibrium band gap. This anomalous behavior can be overcome within the GKBA formalism by coupling to an external bath, which leads to a transition of the EI system toward the normal state. We analyze the long-time evolution of the system and distinguish decay timescales related to dephasing and thermalization.
We study the time evolution of excitonic states after photoexcitation in the one-dimensional spinless extended Falicov-Kimball model. Several numerical methods are employed and benchmarked against each other: time-dependent mean-field simulations, the second-Born approximation (2BA) within the Kadanoff-Baym formalism, the generalized Kadanoff-Baym ansatz (GKBA) implemented with the 2BA, and the infinite time-evolving block decimation (iTEBD) method. It is found that the GKBA gives the best agreement with iTEBD and captures the relevant physics. Excitations to the particle-hole continuum and resonant excitations of the equilibrium exciton result in a qualitatively different dynamics. In the former case, the exciton binding energy remains positive and the frequency of the corresponding coherent oscillations is smaller than the band gap. On the other hand, resonant excitations trigger a collective mode whose frequency is larger than the band gap. We discuss the origin of these different behaviors by evaluating the nonequilibrium susceptibility using the nonthermal distribution and a random phase approximation. The peculiar mode with frequency larger than the band gap is associated with a partial population inversion with a sharp energy cutoff. We also discuss the effects of the cooling by a phonon bath. We demonstrate the real-time development of coherence in the polarization, which indicates excitonic condensation out of equilibrium.
A fast time propagation method for nonequilibrium Green's functions (NEGF) based on the generalized Kadanoff–Baym Ansatz (GKBA) is applied to a lattice system with a symmetry‐broken equilibrium phase, namely an excitonic insulator (EI). The adiabatic preparation of a correlated symmetry‐broken initial state from a Hartree– Fock wave function within GKBA is assessed by comparing with a solution of the imaginary‐time Dyson equation. It is found that it is possible to reach a symmetry‐ broken correlated initial state with nonzero excitonic order parameter by the adiabatic switching (AS) procedure. It is discussed under which circumstances this is possible in practice within reasonably short switching times.
A fast time propagation method for nonequilibrium Green's functions (NEGF) based on the generalized Kadanoff–Baym Ansatz (GKBA) is applied to a lattice system with a symmetry‐broken equilibrium phase, namely an excitonic insulator (EI). The adiabatic preparation of a correlated symmetry‐broken initial state from a Hartree–Fock wave function within GKBA is assessed by comparing with a solution of the imaginary‐time Dyson equation. It is found that it is possible to reach a symmetry‐broken correlated initial state with nonzero excitonic order parameter by the adiabatic switching (AS) procedure. It is discussed under which circumstances this is possible in practice within reasonably short switching times.
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.
ABSTRACT We benchmark nonequilibrium Green's function (NEGF) approaches for interaction quenches in the half‐filled Fermi–Hubbard model in one and two dimensions. We compare fully self‐consistent two‐time Kadanoff–Baym equations (KBE), the generalized Kadanoff–Baym ansatz (GKBA), and the recently developed NEGF‐based quantum fluctuations approach (NEGF‐QF) with second‐order Born (2B) and GW self‐energies. As references, we use DMRG in 1D and time‐dependent perturbation theory at weak coupling. While all methods reproduce the early‐time build‐up of correlations (prethermalization), different deficiencies emerge during the slower relaxation in the long‐time limit: KBE shows overdamped oscillations, GKBA exhibits a negative overshoot of the Fermi‐surface jump, and NEGF‐QF develops a prethermalization plateau with delayed relaxation. In 1D, we find that GKBA + 2B agrees best with DMRG across the explored parameter range, while QF + GW deviates the most, consistent with its reduced self‐consistency. In 2D, all approaches correctly capture the momentum‐dependence of the relaxation dynamics.
Within the nonequilibrium 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 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 correlated states as initial states. Our scheme makes it possible to efficiently separate the calculation of the initial state from the real-time simulation, thus paving the way for enlarging the class of systems and external drivings accessible by the already successful NEGF-GKBA. We demonstrate the accuracy of the method and its improved performance in a model donor-acceptor dyad driven out of equilibrium by an external laser pulse.