On spectral properties of Generalized Kadanoff--Baym Ansatz

The Generalized Kadanoff--Baym Ansatz with mean-field propagators is increasingly used to simulate non-equilibrium quantum fermionic and bosonic systems. Compared with the full Kadanoff--Baym equations, its mean-field propagators substantially reduce computational cost, enabling simulations with computational effort that scales linearly with propagation time. However, the time-diagonal structure of the Generalized Kadanoff--Baym Ansatz obscures spectral properties within the collision integral of the transport equation. Here, we recover and investigate these hidden spectral properties using the extended Generalized Kadanoff--Baym Ansatz. For a Hubbard cluster, we compare ground-state spectral functions obtained with the extended Generalized Kadanoff--Baym Ansatz against those from standard Kadanoff--Baym equations. At moderate interaction strengths, the spectral functions show good agreement. At large interaction strengths, however, significant deviations emerge, and the spectral function obtained with the extended Generalized Kadanoff--Baym Ansatz becomes negative. These results demonstrate that, despite its computational advantages, the Generalized Kadanoff--Baym Ansatz has important limitations in strongly interacting regimes and may produce unphysical spectral properties when interactions become sufficiently large.