Quantum Dynamics Made Fast: Achieving Linear Time-Scaling for Nonequilibrium Green Functions

The accurate description of the nonequilibrium dynamics in correlated quantum-many-body systems remains to be a driving force for current research in condensed-matter physics and beyond.
Among others, the nonequilibrium Green functions (NEGF) method has proven to be a powerful tool to reliably predict the quantum dynamics, without being limited to 1D or spatially homogeneous systems. However, NEGF simulations are computationally expensive due to their T³ scaling with the simulation duration T. With the introduction of the generalized Kadanoff–Baym ansatz^[1] (GKBA) T² scaling could be achieved for second-order Born (SOA) selfenergies^[2], which has substantially extended the scope of NEGF simulations. Recently^[3], we could show that GKBA-NEGF simulations can be performed with order T¹ scaling for SOA, GW, and T-matrix selfenergies, and even for the screened-ladder approximation^[4]. Here, we show numerical results for various many-body approximations and demonstrate that a tremendous computational speed-up can be achieved in practice.

[1] P. Lipavský et al., Phys. Rev. B 34, 6933 (1986)
[2] S. Hermanns et al., Phys. Scr. 2012 014036 (2012)
[3] N. Schlünzen et al.,Phys. Rev. Lett. 124, 076601 (2020)
[4] J.-P. Joost et al., Phys. Rev. B 101, 245101 (2020)