Speaker
Description
Correlated real-time dynamics in large, spatially inhomogeneous quantum systems remain a major challenge for nonequilibrium many-body approaches. Nonequilibrium Green functions (NEGF) provide a systematic and highly accurate framework for addressing this problem, but their practical application has long been limited by the cubic scaling of the computational runtime with the number of time steps, $N_t$. This bottleneck was recently overcome by the G1–G2 scheme [1], which achieves linear scaling in $N_t$. However, numerical instabilities become increasingly more prevalent at stronger coupling, and the explicit propagation of the two-particle Green function incurs a substantial memory overhead. Consequently, time-dependent simulations have so far remained limited to comparatively small systems with basis sizes of order $N_b\sim10^2$.
Here, we introduce a quantum-fluctuation formulation of nonequilibrium Green functions, denoted $\delta$NEGF [2], which addresses these limitations by representing two-particle correlations through fluctuations of field-operator products. The resulting formulation preserves the positivity of reduced density matrices, thereby stabilizing correlated dynamics, eliminates the explicit storage of the two-particle Green function, and maps the dynamics onto a finite ensemble of Hartree–Fock-like trajectories. Combined with a stochastic low-rank decomposition of the correlation functions, $\delta$NEGF substantially reduces the computational and memory requirements of advanced self-energy approximations, including GW and particle-particle as well as particle-hole T-matrix approximations, while retaining linear scaling in $N_t$.
We benchmark $\delta$NEGF against exact and HF-GKBA results for lattice systems and demonstrate its scalability in simulations reaching basis sizes of order $N_b\sim10^4$.
[1] Schlünzen et al., Phys. Rev. Lett. 124, 076601 (2020)
[2] Schroedter et al., arXiv:2606.10773 (2026)