# Efficient Real-Time Path Integrals for Non-Markovian Spin-Boson Models

## TL;DR

This paper introduces a new numerical method for simulating non-Markovian spin-boson models using real-time path integrals, accurately capturing dynamics including revivals caused by environmental memory effects.

## Contribution

The authors reformulate finite memory approximations in path integral simulations to exactly reproduce non-Markovian dynamics, enabling more accurate modeling of complex quantum systems.

## Key findings

- New method accurately reproduces exact dynamics
- Reveals population revivals due to non-Markovian effects
- Enables simulation of previously intractable parameter regimes

## Abstract

Strong coupling between a system and its environment leads to the emergence of non-Markovian dynamics, which cannot be described by a time-local master equation. One way to capture such dynamics is to use numerical real-time path integrals, where assuming a finite bath memory time enables manageable simulation scaling. However, by comparing to the exactly soluble independent boson model, we show that the presence of transient negative decay rates in the exact dynamics can result in simulations with unphysical exponential growth of density matrix elements when the finite memory approximation is used. We therefore reformulate this approximation in such a way that the exact dynamics are reproduced identically and then apply our new method to the spin-boson model with superohmic environmental coupling, commonly used to model phonon environments, but which cannot be solved exactly. Our new method allows us to easily access parameter regimes where we find revivals in population dynamics which are due to non-Markovian backflow of information from the bath to the system.