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Fredholm determinants, full counting statistics and Loschmidt echo for domain wall profiles in one-dimensional free fermionic chains
by Oleksandr Gamayun, Oleg Lychkovskiy, Jean-Sébastien Caux
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Oleksandr Gamayun · Oleg Lychkovskiy |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/1911.01926v1 (pdf) |
| Date submitted: | Nov. 12, 2019, 1 a.m. |
| Submitted by: | Oleksandr Gamayun |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We consider an integrable system of two one-dimensional fermionic chains connected by a link. The hopping constant at the link can be different from that in the bulk. Starting from an initial state in which the left chain is populated while the right is empty, we present time-dependent full counting statistics and the Loschmidt echo in terms of Fredholm determinants. Using this exact representation, we compute the above quantities as well as the current through the link, the shot noise and the entanglement entropy in the large time limit. We find that the physics is strongly affected by the value of the hopping constant at the link. If it is smaller than the hopping constant in the bulk, then a local steady state is established at the link, while in the opposite case all physical quantities studied experience persistent oscillations. In the latter case the frequency of the oscillations is determined by the energy of the bound state and, for the Loschmidt echo, by the bias of chemical potentials.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2020-1-30 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1911.01926v1, delivered 2020-01-30, doi: 10.21468/SciPost.Report.1471
Strengths
2-Comprehensive and elegant exposition of many results scattered in the literature
Weaknesses
Report
The authors derive Fredholm determinant representations for the FCS and the LE, from which in most of the cases they are able to extract exact large-time asymptotic.
Although it is true that most of the results presented here already appeared in some form elsewhere, I found the Fredholm determinant derivation of the FCS and the LE comprehensive, elegant and pedagogically written.
The bound state oscillatory contributions to the current and the entanglement are also clearly emphasized.
I believe that the results presented are ready for publications in their present form.
I spot a few innocent typos, listed below:
-Eq. (7) differential is missing
-Eq. (42), $\varphi\rightarrow\phi$
-Eq. (66), $t\rightarrow\tau$
-Below Eq. (86), I think $N\rightarrow N_f$
Requested changes
See report
Report #1 by Anonymous (Referee 1) on 2020-1-6 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1911.01926v1, delivered 2020-01-06, doi: 10.21468/SciPost.Report.1432
Report
Although the paper is extremely technical, the physical content is clearly explained and accessible to a nonspecialist. This study is a useful addition to the literature and the authors perform an excellent job in comparing with previously known results and indicating the original contributions of this study. Calculations are properly presented (I would make the derivation of Eq. (45) more pedagogical, as it is a central point). I have essentially nothing to criticize about this manuscript, and I think it is suitable for publication in SciPost in the present form.
As a side remark, the authors might find it interesting to compare the a.c. current induced by the defect, which they discuss in this manuscript, with that induced by the superficially similar (but seemingly unrelated) effect studied in P.P. Mazza et al., Phys. Rev. B 99, 180302(R).