Diagrammatic method for many-body non-Markovian dynamics: memory effects and entanglement transitions

TL;DR

This paper introduces a diagrammatic approach to analyze non-Markovian quantum many-body dynamics, revealing how memory effects influence trajectory probabilities and entanglement transitions.

Contribution

It develops a systematic, diagrammatic method to unravel non-Markovian dynamics in many-body systems, extending quantum jump techniques beyond single-body cases.

Findings

Non-Markovianity renormalizes quantum trajectory probabilities.

Memory effects act as perturbations on Markovian dynamics.

Non-Markovianity stabilizes the volume law entanglement phase.

Abstract

We study the quantum dynamics of a many-body system subject to coherent evolution and coupled to a non-Markovian bath. We propose a technique to unravel the non-Markovian dynamics in terms of quantum jumps, a connection that was so far only understood for single-body systems. We develop a systematic method to calculate the probability of a quantum trajectory, and formulate it in a diagrammatic structure. We find that non-Markovianity renormalizes the probability of realizing a quantum trajectory, and that memory effects can be interpreted as a perturbation on top of the Markovian dynamics. We show that the diagrammatic structure is akin to that of a Dyson equation, and that the probability of the trajectories can be calculated analytically. We then apply our results to study the measurement-induced entanglement transition in random unitary circuits. We find that non-Markovianity does not significantly shift the transition, but stabilizes the volume law phase of the entanglement by shielding it from transient strong dissipation.