Measurement induced transitions in non-Markovian free fermion ladders

TL;DR

This paper investigates how non-Markovian effects influence measurement-induced entanglement transitions in coupled free fermion chains, revealing phase behaviors and the relationship between non-Markovianity and entanglement.

Contribution

It introduces a model of coupled fermion chains with non-Markovian dynamics and characterizes the resulting entanglement phases and their dependence on system parameters.

Findings

Pure state: area law phase at low bath hopping, non-area law at high bath hopping.

Logarithmic entanglement scaling suggests conformal phase, with finite-size corrections.

Non-Markovianity correlates with increased entanglement in the system.

Abstract

Recently there has been an intense effort to understand measurement induced transitions, but we still lack a good understanding of non-Markovian effects on these phenomena. To that end, we consider two coupled chains of free fermions, one acting as the system of interest, and one as a bath. The bath chain is subject to Markovian measurements, resulting in an effective non-Markovian dissipative dynamics acting on the system chain which is still amenable to numerical studies in terms of quantum trajectories. Within this setting, we study the entanglement within the system chain, and use it to characterize the phase diagram depending on the ladder hopping parameters and on the measurement probability. For the case of pure state evolution, the system is in an area law phase when the internal hopping of the bath chain is small, while a non-area law phase appears when the dynamics of the bath is fast. The non-area law exhibits a logarithmic scaling of the entropy compatible with a conformal phase, but also displays linear corrections for the finite system sizes we can study. For the case of mixed state evolution, we instead observe regions with both area, and non-area scaling of the entanglement negativity. We quantify the non-Markovianity of the system chain dynamics and find that for the regimes of parameters we study, a stronger non-Markovianity is associated to a larger entanglement within the system.