G1-G2 scheme: Dramatic acceleration of nonequilibrium Green functions simulations within the Hartree-Fock generalized Kadanoff-Baym ansatz

Article

关键词: CORRELATION TIME;    ELECTRON-GAS;    QUANTUM;    EQUATIONS;    RELAXATION;    ENERGY;    APPROXIMATION;    TRANSPORT;    DYNAMICS;    PLASMAS;   

DOI  :  10.1103/PhysRevB.101.245101

来源: SCIE

【 摘 要 】

The time evolution in quantum many-body systems after external excitations is attracting high interest in many fields, including dense plasmas, correlated solids, laser-excited materials, or fermionic and bosonic atoms in optical lattices. The theoretical modeling of these processes is challenging, and the only rigorous quantum-dynamics approach that can treat correlated 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) self energy, which has substantially extended the scope of NEGF simulations. In a recent Letter [Schlunzen et al., Phys. Rev. Lett. 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 the G1 -G2 scheme. This allows one to perform the same simulations with order T-1 scaling, both for SOA and GW self energies 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 self energies, including the T matrix in the particle-particle and particle-hole channels and the dynamically-screened-ladder approximation. Finally, we demonstrate that, for all self energies, 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, even for Hubbard systems.

【 授权许可】

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