Efficient real-time calculations using optimal sum-over-pole schemes

Describing the real-time dynamics of correlated quantum systems is challenging due to the increasing computational cost with simulation time, making long-time simulations impractical. The Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm [1,2] offers an efficient way to represent real-time data as complex exponentials. We show how ESPRIT can extract the information contained in short-time dynamics to reliably predict long-time behavior and determine the minimum time interval required for accurate results. While this method is applicable to any real-time approach or observable, we apply it to propagators and Green’s functions from quantum Monte Carlo, where ESPRIT also acts as a noise filter. By leveraging a compact exponential representation, we demonstrate how these observables can be efficiently evaluated and how impurity solvers can be formulated on minimal time spans. This allows us to address problems with long coherence times, such as Kondo physics, which are difficult for propagation-based methods.

[1] R.Roy and T. Kailath, IEEE Trans. Acoust., Speech, Signal Process. 37, 984 (1989)

[2] T. Sarkar and O. Pereira, IEEE Antennas Propag. Mag. 37, 48 (1995)