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Exact solution for the Lindbladian dynamics for the open XX spin chain with boundary dissipation
by Kohei Yamanaka and Tomohiro Sasamoto
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Submission summary
| Authors (as registered SciPost users): | Kohei Yamanaka |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202105_00008v3 (pdf) |
| Date accepted: | 2023-03-15 |
| Date submitted: | 2023-02-17 06:42 |
| Submitted by: | Yamanaka, Kohei |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We obtain exact formulas for the time-dependence of a few physical observables for the open XX spin chain with Lindbladian dynamics. Our analysis is based on the fact that the Lindblad equation for an arbitrary open quadratic system of N fermions is explicitly solved in terms of diagonalization of a 4N×4N matrix called structure matrix by following the scheme of the third quantization. We mainly focus on the time-dependence of magnetization and spin current. As a short time behavior at a given site, we observe the plateau regime except near the center of chain. Basic features of this are explained by the light-cone structure created by propagations of boundary effects from the initial time, but we can explain their more detailed properties analytically using our exact formulas. On the other hand, after the plateau regime, the magnetization and spin current exhibit a slow decay to the steady state values described by the Liouvillian gap. We analytically establish its 1/N^3 scaling and also determine its coefficient.
Author comments upon resubmission
We have revised the manuscript "Exact solution for the Lindbladian dynamics for the open XX spin chain with boundary dissipation" according to the referees' comments. We believe we have been able to answer to almost all the comments and to produce an improved version of the paper.
List of changes
•We have improved the following several points in our manuscript in order to make our paper more accessible to non-technically inclined readers.
•We wrote the final results in terms of the model parameters to be understood by non-technically inclined readers.
•We added a few more explanations about motivations and summaries of our discussions.
•We removed the unnecessary abbreviations and definitions.
• We corrected minor typos/modify sentences.
Published as SciPost Phys. 14, 112 (2023)