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Spin-1/2 XX chains with modulated Gamma interaction
by Mohammad Abbasi, Saeed Mahdavifar, Mostafa Motamedifar
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Saeed Mahdavifar |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202408_00019v2 (pdf) |
| Date submitted: | 2024-10-08 20:26 |
| Submitted by: | Mahdavifar, Saeed |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We study the spin-1/2 XX chain with a modulated Gamma interaction (GI), which results from the superposition of uniform and staggered Gamma terms. We diagonalize the Hamiltonian of the model exactly using the Fermionization technique. We then probe the energy gap and identify the gapped and gapless regions. We also examine the staggered chiral, staggered nematic and dimer order parameters to determine the different phases of the ground state phase diagram with their respective long-range orders. Our findings indicate that the model undergoes first-order, second-order, gapless-gapless, and gapped-gapped phase transitions.
Author comments upon resubmission
We thank referee for his/her constructive comments
on our manuscript. In the revised version of our manuscript we tried
to address all points of criticisms (shown in red color) and do make presentation of
our results more clear and transparent.
We hope, that with performed changes, the manuscript fulfills
requirements to be accepted for publication in "Scipost Physics Core".
Sincerely,
Saeed Mahdavifar
List of changes
We would like to thank the Reviewer for reviewing the paper. In addition, we thank her/his constructive comments concerning our manuscript.
First comment:
page 2: $\alpha-RuCl_{3}$ is misprinted.
Our answer:
Thank you. The corrections have been made in the updated version of the manuscript.
Second comment:
Figure 1 is referenced at the end of Section 1, but not really discussed. I feel that it would be appropriate to add such a discussion.
Our answer:
We appreciate the referee's comment. We have included a discussion about this figure in the last paragraph of Section 1, highlighted in red.
Third comment:
The asymptotic behavior in Fig. 2(c) looks linear to me ....
Our answer:
We appreciate the referee's valuable feedback. Upon re-evaluating our results, we found the scaling behavior to be linear. Please refer to the third paragraph of the Results section in the revised version.
Fourth comment:
Clarify meaning of sign changed of the staggered chiral order parameter .
Our answer:
Thank you for your comment. Please refer to the third paragraph following Eq. (9) in the revised manuscript. Additionally, we have replaced the topological critical line with the gapless-gapless phase transition line.
Current status:
Reports on this Submission
Report
With their revised version, the authors have made some improvements to their manuscript. It is now a pleasure to recommend publication in SciPost Physics Core under the condition that the authors correct the following item: The new section on page 8 still does not convince me that the sign change of the chiral order parameter $\chi_s$ has any relation with a phase transition or critical behavior. A phase transition is characterized by a singularity in the derivatives of the free energy and a critical point by a divergent correlation length. I see no evidence for either one. Speaking of "transition" or "region" would be acceptable, but terminology such as "phase transition" or "critical line" should be avoided in this context. I am afraid that this remains a recurrent issue in the manuscript, i.e., not only on page 8, but also the last line of the abstract, Fig. 1 and its caption, the Conclusion, and possibly other places in the manuscript.
I noticed a few further minor issues when rereading the manuscript that I list under "Requested changes".
Requested changes
Item 1 is mandatory. The remaining ones are suggestions to eliminate errors during production.
1- Remove terminology such as "phase transition" or "critical line" in relation with the sign change of the chiral order parameter $\chi_s$.
2- Third paragraph of page 2 and title of Ref. [13]: Double-check spacing in "$Na_2Co_2TeO_6$ (the "$Na$").
3- Immediately afterwards: delete stray space between "[12,13]" and the full stop ".".
4- All figure captions: The "(color online)" is not needed.
5- 4th line of section 3: "emerge" $\to$ "emerges".
6- 7th line of section 3: "will be happened" $\to$ "will happen".
7- Caption of Fig. 2: a) "When system" $\to$ "When the system" (lines 2, 3, and 4). b) Correct spelling of "gapful" on line 4.
8- 3rd line of 3rd paragraph on page 8: "It is known that a chiral" $\to$ "A chiral" (style).
9- Caption of Fig. 3: a) "the $\alpha$" $\to$ "$\alpha$" (lines 1, 3, and 4). b) "in absence" $\to$ "in the absence" (lines 3 and 4). c) "the $\Gamma_1$" $\to$ "$\Gamma_1$" (lines 5 and 7). d) "in presence" $\to$ "in the presence" (lines 6, 7, and 10). e) "derivative if the" $\to$ "derivative of the" (line 8). f) "the $\Gamma_0$" $\to$ "$\Gamma_0$" (line 10).
10- 5th line of 3rd paragraph on page 10: "it's" $\to$ "its".
11- 11th line of 3rd paragraph on page 10: "is happen" $\to$ "happens".
12- Caption of Fig. 4: a) "the $\alpha$" $\to$ "$\alpha$" (lines 2, 3, and 4). b) "in absence" $\to$ "in the absence" (lines 2, 3, and 4). c) "the $\Gamma_1$" $\to$ "$\Gamma_1$" (lines 6, 7, and 9). d) "in presence" $\to$ "in the presence" (lines 6, 7, and 9). e) "derivative if the" $\to$ "derivative of the" (line 10).
13- Caption of Fig. 5: a) "the $\Gamma_1$" $\to$ "$\Gamma_1$" (lines 1 and 3). b) "in presence" $\to$ "in the presence" (lines 1-2 and 3).
14- 4 lines below Eq. (11): in presence" $\to$ "in the presence".
15- Properly itemize the starred items on the second half of page 13 using the LaTeX itemize environment.
16- Refs. [8,9,21] are the only ones that combine two references. Why not split these into two?
17- It seems that Ref. [19] is not cited. $\Rightarrow$ remove?
18- It seems that Refs. [20,21] are cited only after Ref. [22]. $\Rightarrow$ reorder?
19- Title of Ref. [27]: "$KCuPO_4.H_2O$"$\to$ "$KCuPO_4\cdot H_2O$".
20- Authors of Ref. [28]: "K. W.Baldwin, K. W. West" $\to$ "K.W. Baldwin, K.W. West" (spacing).
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)