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Measurement induced transitions in non-Markovian free fermion ladders
by Mikheil Tsitsishvili, Dario Poletti, Marcello Dalmonte, Giuliano Chiriacò
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Giuliano Chiriacò · Marcello Dalmonte · Mikheil Tsitsishvili |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202312_00020v2 (pdf) |
| Date accepted: | 2024-03-04 |
| Date submitted: | 2024-02-27 11:24 |
| Submitted by: | Chiriacò, Giuliano |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
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.
Author comments upon resubmission
We thank you for handling the manuscript and both the Referees for the positive comments on the resubmitted version of our manuscript.
Regarding the Report of Referee 2, we had actually not understood exactly what the Referee meant in the previous report. We are grateful to the Referee for clarifying it. However, the suggested method of using Gaussian states for the time evolution and then calculating the full density matrix along each trajectory, still contains an exponential complexity like the ED method. This makes it more costly than the method purely based on correlations of Gaussian states, and also more costly than the ED method, which does not require a parallel evolution and then an average over different trajectories. We would also note that the proposed method is feasible for $L\leq12$ in a single chain, which becomes $L\leq6$ in the ladder model we consider, i.e. close to the systems sizes we reach with ED and smaller than the system sizes studied with the purely Gaussian-based method. We have added a remark on this in the text, along with a table summarizing the computational complexity of the different methods.
We hereby resubmit the manuscript with the mentioned change.
Yours sincerely,
M. Tsitsishvili
D. Poletti
M. Dalmonte
G. Chiriacò
Published as SciPost Phys. Core 7, 011 (2024)