Low rank compression in the numerical solution of the nonequilibrium Dyson equation

A quantum Boltzmann equation for strongly correlated electrons

“…Before that, we conclude this section with a side remark: It is known even in equilibrium that the self-consistent solution of the Dyson equation with a skeleton self energy functional can have multiple unphysical solutions. 51 However, a possible multi-valuedness of the functional (34) will not be a problem here. The functions A k (ω, t), F k (ω, t), and Σ k (ω, t) evolve continuously as a function of time, so that even if unphysical steady-state solutions exist for a given distribution function, the physical solution is always selected by the requirement of continuity and the initial condition.…”

“…For weakly interacting systems, the perturbatively controlled generalized Kadanoff-Baym Ansatz (GKBA) 31 has recently been set up to reach O(t max ) scaling of the computational effort. 32 For strongly correlated systems, a systematic truncation 33 or compact compression 34 of the memory kernel in the Kadanoff-Baym equations provide interesting perspectives, but so far the investigation of many fundamental questions has remained out of reach because of the O(t 3 max ) scaling. It would therefore be desirable to formulate a QBE which incorporates the simplifications due to the timescale separation, but does not rely on quasiparticle or perturbative approximations.…”