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Mapping a dissipative quantum spin chain onto a generalized Coulomb gas
by Oscar Bouverot-Dupuis
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Oscar Bouverot-Dupuis |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2403.06618v1 (pdf) |
| Date submitted: | April 9, 2024, 3:29 p.m. |
| Submitted by: | Oscar Bouverot-Dupuis |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| 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.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2024-5-31 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2403.06618v1, delivered 2024-05-31, doi: 10.21468/SciPost.Report.9162
Strengths
1- exact mapping between a dissipative spin chain and a generalized Coulomb gas 2- RG equations are solved for sub- and superohmic baths 3- well written and well explained 4- an intuitive mechanism for the dissipation-driven quantum phase transition is developed
Report
This work provides a link between a quantum many-body problem that is of current interest and a stat-mech problem that has an intuitive understanding. The paper includes sufficient details to follow the derivation, but also puts a lot of emphasis in describing the physical picture in simple words. I enjoyed reading the paper and learned a lot from the discussion. All in all, I recommend publication in SciPost Physics.
Requested changes
1- I am wondering about the decay of the dissipation kernel $D(x,\tau)$ in Eq. (14) and its dependence on the bath exponent $s$. For $\nu=0$ it becomes $D(x,\tau)\propto \delta(x)/(\tau/\tau_c)^{2+s}$. In particular, for an ohmic bath with $s=1$ this leads to a retarded interaction that decays as $1/\tau^3$. I always thought that an ohmic bath corresponds to a temporal decay $\propto 1/\tau^2$, as it is also the case in Ref. [33] (a closely related paper by the author). It would be good to clarify this difference to the author's previous work (or correct it if it is a mistake).
2- On page 8 [below Eq. (20)], the author writes $D(r-r)$. Isn't it just $D(r)$?
3- First line on page 11 [above Eq. (24)]: The formatting of the in-line equation $U=\dots$ is not clear because of the minus sign in front of $V_c(r)$. Can one just put it in front of the integral?
4- On page 12 [the line below Eq. (27)]: I assume it is $K_R$ instead of $K_r$, right?
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Report #1 by Anonymous (Referee 1) on 2024-5-3 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2403.06618v1, delivered 2024-05-03, doi: 10.21468/SciPost.Report.8974
Strengths
- derivation of a mapping of the Caldeira-Leggett action of a quantum sine-Gordon model coupled to a harmonic oscillator bath to a classical generalized Coulomb gas.
- renormalization group study of the Berezinskii-Kosterlitz-Thouless transition of the generalized Coulomb gas
Report
The abstract and main results section describe the main findings which are also exposed in the first paragraph of the conclusions. The relevant previous work is covered in Refs. [21-34] and Ref. [38].
The article establishes an interesting link between quantum phase transitions in the presence of dissipation induced by a harmonic bath and classical statistical mechanics of generalized Coulomb gases. Phase transitions in dissipative quantum mechanics have undergone a recent regain of attention from theoretician, and a connection with a well studied subject such as Coulomb gas is likely to yield quick progress. An aspect which is not touched in the paper, but considered in Refs. [30,31] for a different model is the characterization of the phases in which dissipation dominates. The present article is likely to stimulate such studies. I thus recommend publication in SciPost.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)