Designing Real-Time Quantum Impurity Solvers with Data-Driven Sum-over-Pole Representations

Simulating the real-time dynamics of quantum systems is notoriously difficult due to the rapid growth of computational complexity with simulation time. This limits the applicability of state-of-the-art quantum impurity solvers for strongly correlated systems with long coherence times, where describing the full dynamics beyond short-time responses is often impractical. We show [1] that the long-time behavior is often encoded in short-time dynamics and can be extracted with data-driven approaches. We incorporate these ideas into real-time quantum impurity solvers by efficiently representing real-time data as sums of complex exponentials. This compact representation drastically reduces computational costs for core numerical tasks, such as real-time propagation, evaluation of high-dimensional integrals, self-consistency iterations, and post-processing. Using the Anderson impurity model, we show how observables can be accurately evaluated, enabling access to long coherence time phenomena, such as Kondo physics in and out of equilibrium, that remain challenging for conventional quantum impurity solvers.

[1] Erpenbeck et al., arXiv:2506.13760 (2025)