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Entanglement and quench dynamics in the thermally perturbed tricritical fixed point
by Csilla Király, Máté Lencsés
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Máté Lencsés |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2506.19596v3 (pdf) |
| Date submitted: | Nov. 5, 2025, 10:23 a.m. |
| Submitted by: | Máté Lencsés |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We consider the Blume--Capel model in the scaling limit to realize the thermal perturbation of the tricritical Ising fixed point. We develop a numerical scaling limit extrapolation for one-point functions and R\'enyi entropies in the ground state. In a mass quench scenario, we found long-lived oscillations despite the absence of explicit spin-flip symmetry breaking or confining potential. We construct form factors of branch-point twist fields in the paramagnetic phase. In the scaling limit of small quenches, we verify form factor predictions for the energy density and leading magnetic field using the dynamics of one-point functions, and branch-point twist fields using the dynamics of R\'enyi entropies.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
We are grateful to the Referees for their constructive criticism and suggestions for improvement. Below we present the full list of changes in view of the referee reports. We also reply to the Referees separately below their report, explaining the changes made in detail.
List of changes
Pg.2. $E_7$ and $E_8$ scattering therioes are also mentioned as Toda field thoeries.
Pg.2 Added refs. [19] [20]
Pg.2. We removed the adjective: "persistent" from the sentence starting as "Within the timescales accesible to us..."
Pg.3. Ref [78] from the previous version is moved here, and now is ref. [35]
Pg.4 Comment on entanglemen along the massless perturbation and Ref.[56] added.
Pg. 4 Caption of Table 1. now contians our notation for the conformal weights.
In earlier version we used both $h_{\mathcal{O}}$ and $\Delta_{\mathcal{O}}$ to denote chiral conformal weights. In the new verions we use only $\Delta_{\mathcal{O}}$ to denote chiral weights throughout the paper.
Pg. 5 "Blume–Capem" is replaced to "Blume-Capel" in the beginning of 2.3
Pg. 6 Added ref [70]
Pg. 6 Last before paragraph of Subsec. 2.3 rephrased
Pg. 9 $\mathcal{E}$ is changed to $\epsilon$ in Table 2.
Pg. 11-12 Paragraphs rewritten starting from the one containing eq. (23) to the one after eq. (24)
Pg. 12-13 Rewritten paragraph starting on the bottom of Pg. 12.
Pg. 16 Sentence on the $\Delta$-theorem rewritten, reference [80] added.
Pg. 18 "$\cdot$" added in front of powers of $10$ in Table 4.
Pg. 20 Last paragraph of 3.4.2. rewritten, ref. [84] added.
Pg. 20-21 Historical introduction added in the beginning of Section 4., with addition of refs. [31],[85], [86] and [89].
Pg. 21 Subsection 4.1 is renamed to "Post-quench perturbation theory for small quenches"
Pg. 21 First paragraph of 4.1.1 removed.
Pg. 23 Paragraph after eq. (85) rewritten, refs [34][35] added
Pg. 27-28. Paragraphs reformulated, starting after: ".....expectation value in
the "von Gehlen tricritical point"". to "Considering odd perturbations...."; references [84],[91],[92],[94],[95] added
Pg. 33-34 Appendix B.3 on the composite twist field solution and the corresponding $\Delta$ sum rule added.
Pg.2 Added refs. [19] [20]
Pg.2. We removed the adjective: "persistent" from the sentence starting as "Within the timescales accesible to us..."
Pg.3. Ref [78] from the previous version is moved here, and now is ref. [35]
Pg.4 Comment on entanglemen along the massless perturbation and Ref.[56] added.
Pg. 4 Caption of Table 1. now contians our notation for the conformal weights.
In earlier version we used both $h_{\mathcal{O}}$ and $\Delta_{\mathcal{O}}$ to denote chiral conformal weights. In the new verions we use only $\Delta_{\mathcal{O}}$ to denote chiral weights throughout the paper.
Pg. 5 "Blume–Capem" is replaced to "Blume-Capel" in the beginning of 2.3
Pg. 6 Added ref [70]
Pg. 6 Last before paragraph of Subsec. 2.3 rephrased
Pg. 9 $\mathcal{E}$ is changed to $\epsilon$ in Table 2.
Pg. 11-12 Paragraphs rewritten starting from the one containing eq. (23) to the one after eq. (24)
Pg. 12-13 Rewritten paragraph starting on the bottom of Pg. 12.
Pg. 16 Sentence on the $\Delta$-theorem rewritten, reference [80] added.
Pg. 18 "$\cdot$" added in front of powers of $10$ in Table 4.
Pg. 20 Last paragraph of 3.4.2. rewritten, ref. [84] added.
Pg. 20-21 Historical introduction added in the beginning of Section 4., with addition of refs. [31],[85], [86] and [89].
Pg. 21 Subsection 4.1 is renamed to "Post-quench perturbation theory for small quenches"
Pg. 21 First paragraph of 4.1.1 removed.
Pg. 23 Paragraph after eq. (85) rewritten, refs [34][35] added
Pg. 27-28. Paragraphs reformulated, starting after: ".....expectation value in
the "von Gehlen tricritical point"". to "Considering odd perturbations...."; references [84],[91],[92],[94],[95] added
Pg. 33-34 Appendix B.3 on the composite twist field solution and the corresponding $\Delta$ sum rule added.
Current status:
Has been resubmitted
Reports on this Submission
Report
The authors did not think much on the comments in my report and took them into account only very partially. In particular, their reply states that they agree with me on the fact that “any viable computation should be done in the post-quench basis”. I did not say anything like that. What I said is that the post-quench basis has to be used in the NON-PERTURBATIVE framework of Ref. [89]. As for PERTURBATIVE calculations, I clearly recalled that, as anyone understands, any perturbation theory can only be performed around the unperturbed theory. Hence, perturbation theory in the quench size $\lambda$ can only be done around $\lambda=0$, which is the theory with no quench (pre-quench theory).
The authors write in the revised version that “the pre-quench approach has limited validity”, as if they knew of some perturbative approach which at finite order can have unlimited validity. I clearly explained in my report why replacing in the first order perturbative expressions the pre-quench matrix elements with the post-quench ones is useful and certainly worth doing in order to enlarge (by a finite amount) the time window of quantitative accuracy of the perturbative results. The reason is that the replacement introduces corrections (in particular to the particle masses) which in perturbation theory would arise at higher order. It is clear, however, that this replacement by hand does not define a new perturbation theory, which cannot exist.
These points are obvious to anyone familiar with the notion of perturbation theory and do not require specific expertise on quantum quenches. Pretending the contrary astonishes the educated reader and is worthless: the correct presentation of the results only involves text editing and does not require additional analytical or numerical work.
The authors write in the revised version that “the pre-quench approach has limited validity”, as if they knew of some perturbative approach which at finite order can have unlimited validity. I clearly explained in my report why replacing in the first order perturbative expressions the pre-quench matrix elements with the post-quench ones is useful and certainly worth doing in order to enlarge (by a finite amount) the time window of quantitative accuracy of the perturbative results. The reason is that the replacement introduces corrections (in particular to the particle masses) which in perturbation theory would arise at higher order. It is clear, however, that this replacement by hand does not define a new perturbation theory, which cannot exist.
These points are obvious to anyone familiar with the notion of perturbation theory and do not require specific expertise on quantum quenches. Pretending the contrary astonishes the educated reader and is worthless: the correct presentation of the results only involves text editing and does not require additional analytical or numerical work.
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