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Mapping a dissipative quantum spin chain onto a generalized Coulomb gas
by Oscar Bouverot-Dupuis
Submission summary
| Authors (as registered SciPost users): | Oscar Bouverot-Dupuis |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2403.06618v3 (pdf) |
| Date submitted: | 2024-10-16 13:09 |
| Submitted by: | Bouverot-Dupuis, Oscar |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
An XXZ spin chain at zero magnetization is subject to spatially correlated baths acting as dissipation. We show that the low-energy excitations of this model are described by a dissipative sine-Gordon field theory, i.e. a sine-Gordon action with an additional long-range interaction emerging from dissipation. The field theory is then exactly mapped onto a generalized Coulomb gas which, in addition to the usual integer charges, displays half-integer charges that originate from the dissipative baths. These new charges come in pairs linked by a charge-independent logarithmic interaction. In the Coulomb gas picture, we identify a Berezinsky-Kosterlitz-Thouless-like phase transition corresponding to the binding of charges and derive the associated perturbative renormalization group equations. For superohmic baths, the transition is due to the binding of the integer charges, while for subohmic baths, it is due to the binding of the half-integer charges, thereby signaling a dissipation-induced transition.
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Author comments upon resubmission
I would like to thank both referees for submitting a second round of valuable comments on my article. Following their suggestions and comments, I have edited certain parts of the manuscript. Below, I present a point-by-point response to all the queries of the referees.
Yours sincerely,
Oscar Bouverot-Dupuis
List of changes
Response to referee #1:
1) The second referee also raised the issue of the limit ν→0 (point 1) and the authors have responded that the Green's function of the bath operator (−ν2∂2x−∂2τ+Ω2)−1 does not deform confinuously into the one on the local bath operator (−∂2τ+Ω2)−1. [...] I suggest the authors replace their footnote with a derivation of the delta distribution limit of the kernel from Eq. (12) and that final version of the manuscript gets published in SciPost.
Answer : I would like to sincerely thank the referee for making what I believe is a very valuable addition to the manuscript. I have put the derivation of the ν→0 limit in appendix A.2 and referred to it in the last paragraph of section 3.
Response to referee #2:
"1) The author also discusses the implications of the ν→0 limit in Section 6. Because this discussion is rather technical, the meaning is not fully clear to me. As I understand this part, the Coulomb gas picture applies here as well, with the only difference that the interaction in Eq. (23) becomes local in space (and remains nonlocal in time). Is that correct?"
Answer : Yes, that is fully correct. In order to make this clearer, I have rewritten the beginning of the second paragraph of Section 6.
2) In the introduction, the author reviews how the Coulomb-gas picture had been applied to generalized XY models, but I do not find any discussion of applications to dissipative systems. In the past, dissipation effects had also been studied in the context of Josephson junctions. For example, the Coulomb gas picture is mentioned for a single dissipative junction [Schmid, Phys. Rev. Lett. 51, 1506 (1983)] or for arrays of dissipative junctions [Bobbert, Fazio, Schön, Zimanyi, Phys. Rev. B 41, 4009 (1990)], but probably also in other works. It would be fair to review also relevant work including dissipation and to check if there are any similarities to the present work."
Answer: I thank the referee for pointing these articles out. I have also found some relevant references in Monte-Carlo studies of dissipative quantum systems. I have included them in the second to last paragraph of section 1, starting from "It is worth mentioning that...". I also discuss the similarities and discrepancies with my work.