History is the best guide to the future: propagating non-Markovian memory effects across spacetime with long-range tensor network models for open quantum systems*

A number of biological structures have the ability to coordinate optically induced electronic processes and operate in a regime where the usual assumptions of a Markovian bath do not hold.

The environment-mediated structural signals play a major role in allostery and it has been suggested that similar spatially distant effects could play a role in light-driven energy and charge transport processes.

However it has been difficult to model non-local spatio-temporal effects as one needs to keep track of the environment response to the system over time.

We use a numerically exact method relying on a Matrix Product State representation of the quantum state of a system and its environment to keep track of the bath explicitly.

Applied to an example motivated by photosynthetic systems with an interaction that depends on the spatial structure of a two-site system this method predicts a non-Markovian dynamics where long-range couplings induce correlations between the system and the environment.

The environment dynamics can be naturally extracted from our method and shine a light on long time feedback effects that are responsible for observed non-Markovian recurrences in the system eigen-populations, and show clear signs of the environment having stored information about the early time motion.