Learning the non-Markovian features of subsystem dynamics

TL;DR

This paper uses tensor networks and machine learning to analyze the non-Markovian features of local subsystem dynamics in quantum many-body systems, revealing how criticality influences Markovian behavior.

Contribution

It introduces a method to extract and characterize dynamical maps for subsystems in quantum chains, providing insights into non-Markovianity and long-term forecasting.

Findings

Criticality leads to more Markovian long-time behavior.

The approach can forecast long-time dynamics beyond direct simulation.

A new measure of non-Markovianity based on dynamical map distance.

Abstract

The dynamics of local observables in a quantum many-body system can be formally described in the language of open systems. The problem is that the bath representing the complement of the local subsystem generally does not allow the common simplifications often crucial for such a framework. Leveraging tensor network calculations and optimization tools from machine learning, we extract and characterize the dynamical maps for single- and two-site subsystems embedded in an infinite quantum Ising chain after a global quench. We consider three paradigmatic regimes: integrable critical, integrable non-critical, and chaotic. For each we find the optimal time-local representation of the subsystem dynamics at different times. We explore the properties of the learned time-dependent Liouvillians and whether they can be used to forecast the long-time dynamics of local observables beyond the times accessible through direct quantum many-body numerical simulation. Our procedure naturally suggests a novel measure of non-Markovianity based on the distance between the quasi-exact dynamical map and the closest CP-divisible form and reveals that criticality leads to the closest Markovian representation at large times.