Nonequilibrium Green Function Simulations for Large Systems

Nonequilibrium Green Functions (NEGF) are a powerful tool for accurately simulating the dynamics of correlated many-body systems. Their main disadvantage—the cubic scaling of the CPU time with the number of time steps—could recently be overcome by introducing the G1–G2 scheme [1], which allowed us to achieve linear scaling. However, it has its own limitations as instabilities become more prevalent, for example, with increasing coupling strength. Moreover, the propagation of the two-particle Green function requires a large amount of computer memory, which, so far, has restricted time-dependent simulations to small systems with fewer than 150 basis states. Here, we introduce an NEGF-based quantum fluctuations (NEGF-QF) approach, building upon earlier works [2], which solves these issues by efficiently factorizing the two-particle Green function. This approach not only significantly reduces computational costs for advanced self-energy approximations, such as GW and the T-matrix, but also facilitates straightforward parallelization, making simulations possible for nonequilibrium systems with ten thousand basis states. We demonstrate the effectiveness of the NEGF-QF for large lattice systems, with both local Hubbard and long-range Coulomb interactions.

[1] N. Schlünzen et al., Phys. Rev. Lett. 124, 076601 (2020)

[2] E. Schroedter et al., Cond. Matt. Phys. 25, 23401 (2022)