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تسجيل مستخدم جديدAchieving the Ultimate Scaling Limit for Nonequilibrium Green Functions Simulations
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The dynamics of strongly correlated fermions following an external excitation reveals extremely rich collective quantum effects. Examples are fermionic atoms in optical lattices, electrons in correlated materials, and dense quantum plasmas. Presently, the only quantum-dynamics approach that rigorously describes these processes in two and three dimensions is nonequilibrium Green functions (NEGF). However, NEGF simulations are computationally expensive due to their $T^3$ scaling with the simulation duration $T$. Recently, $T^2$ scaling was achieved with the generalized Kadanoff--Baym ansatz (GKBA) which has substantially extended the scope of NEGF simulations. Here we present a novel approach to GKBA-NEGF simulations that is of order $T$, and demonstrate its remarkable capabilities.
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The time evolution in quantum many-body systems after external excitations is attracting high interest in many fields. The theoretical modeling of these processes is challenging, and the only rigorous quantum-dynamics approach that can treat correlat
ed fermions in two and three dimensions is nonequilibrium Green functions (NEGF). However, NEGF simulations are computationally expensive due to their $T^3$-scaling with the simulation duration $T$. Recently, $T^2$-scaling was achieved with the generalized Kadanoff--Baym ansatz (GKBA), for the second-order Born (SOA) selfenergy, which has substantially extended the scope of NEGF simulations. In a recent Letter [Schlunzen textit{et al.}, Phys. Rev. Lett. textbf{124}, 076601 (2020)] we demonstrated that GKBA-NEGF simulations can be efficiently mapped onto coupled time-local equations for the single-particle and two-particle Green functions on the time diagonal, hence the method has been called G1--G2 scheme. This allows one to perform the same simulations with order $T^1$-scaling, both for SOA and $GW$ selfenergies giving rise to a dramatic speedup. Here we present more details on the G1--G2 scheme, including derivations of the basic equations including results for a general basis, for Hubbard systems and for jellium. Also, we demonstrate how to incorporate initial correlations into the G1--G2 scheme. Further, the derivations are extended to a broader class of selfenergies, including the $T$ matrix in the particle--particle and particle--hole channels, and the dynamically screened-ladder approximation. Finally, we demonstrate that, for all selfenergies, the CPU time scaling of the G1--G2 scheme with the basis dimension, $N_b$, can be improved compared to our first report: the overhead compared to the original GKBA, is not more than an additional factor $N_b$.
The nonequilibrium dynamics of strongly-correlated fermions in lattice systems have attracted considerable interest in the condensed matter and ultracold atomic-gas communities. While experiments have made remarkable progress in recent years, there r
emains a need for the further development of theoretical tools that can account for both the nonequilibrium conditions and strong correlations. For instance, time-dependent theoretical quantum approaches based on the density matrix renormalization group (DMRG) methods have been primarily applied to one-dimensional setups. Recently, two-dimensional quantum simulations of the expansion of fermions based on nonequilibrium Green functions (NEGF) have been presented [Schluenzen et al., Phys. Rev. B 93, 035107 (2016)] that showed excellent agreement with the experiments. Here we present an extensive comparison of the NEGF approach to numerically accurate DMRG results. The results indicate that NEGF are a reliable theoretical tool for weak to intermediate coupling strengths in arbitrary dimensions and make long simulations possible. This is complementary to DMRG simulations which are particularly efficient at strong coupling.
This article presents an overview on recent progress in the theory of nonequilibrium Green functions (NEGF). NEGF, presently, are the only textit{ab-initio} quantum approach that is able to study the dynamics of correlations for long times in two and
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