Diagrammatic method for many-body non-Markovian dynamics: memory effects and entanglement transitions
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.
Keywords
Cite
@article{arxiv.2302.10563,
title = {Diagrammatic method for many-body non-Markovian dynamics: memory effects and entanglement transitions},
author = {Giuliano Chiriacò and Mikheil Tsitsishvili and Dario Poletti and Rosario Fazio and Marcello Dalmonte},
journal= {arXiv preprint arXiv:2302.10563},
year = {2023}
}