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

Riku Tuovinen, Denis Golež, Michael Schüler, Philipp Werner, Martin Eckstein, Michael A. Sentef

Published Aug 3, 2018• 9 citations
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Abstract

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.

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Contributions to Plasma Physics•Jan 15, 2026•1 citation
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.
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.
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 reconsider the Generalized Kadanoff–Baym Ansatz (GKBA) approximation for non-equilibrium Green’s functions and extend it to self-consistently define an equilibrium correlated (within GKBA) state in closed systems. The advantage of the proposed prescription is to avoid the preparation of the initial equilibrium correlated state via adiabatic switching-on of the correlations. A simple model system, namely a Hubbard-dimer, is used to illustrate aspects of the computational implementation and performance of the new scheme.
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.