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

• URL: http://arxiv.org/abs/2302.10563v3
• Date: Tue, 12 Sep 2023 07:52:42 GMT
• Title: Diagrammatic method for many-body non-Markovian dynamics: memory effects and entanglement transitions
• Authors: Giuliano Chiriac\`o and Mikheil Tsitsishvili and Dario Poletti and Rosario Fazio and Marcello Dalmonte
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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