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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/2403.06618v2 (pdf) |
| Date submitted: | 2024-06-30 00:15 |
| 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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- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
I would like to thank both the referees for their valuable comments and appreciation of the results shown in the 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
"1- I am wondering about the decay of the dissipation kernel D(x,τ) in Eq. (14) and its dependence on the bath exponent s. For ν=0 it becomes D(x,τ)∝δ(x)/(τ/τc)2+s. In particular, for an ohmic bath with s=1 this leads to a retarded interaction that decays as 1/τ3. I always thought that an ohmic bath corresponds to a temporal decay ∝1/τ2, 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)."
Answer : Thank you for pointing out this issue. The bath Kernel D(x,τ) is, roughly speaking, the Green's function of the bath operator G−1. For local baths, G−1 is the one dimensional operator G−11=−∂2τ+Ω2, while for non-local bath it is the two dimensional operator G−12=−v2∂2x−∂2τ+Ω2. It turns out that, as v is taken to 0, the Green's function G2 does not go to G1. This means that to study the v=0 case, one cannot directly set v=0 in the bath kernel D(x,τ) written in the article, but one has rather to rederive its expression from the microscopic model with v=0. With this in mind, local ohmic baths do indeed correspond to a temporal decay ∝1/τ2. Page 7 has been corrected accordingly and a footnote has also been added.
"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=… is not clear because of the minus sign in front of Vc(r). Can one just put it in front of the integral?
4- On page 12 [the line below Eq. (27)]: I assume it is KR instead of Kr, right?"
Thanks for spotting these typos, they have been corrected.