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Quantum tricriticality of incommensurate phase induced by quantum domain walls in frustrated Ising magnetism
by Zheng Zhou, Dong-Xu Liu, Zheng Yan, Yan Chen, Xue-Feng Zhang
This is not the latest submitted version.
|As Contributors:||Xue-Feng Zhang · Zheng Zhou|
|Arxiv Link:||https://arxiv.org/abs/2005.11133v3 (pdf)|
|Date submitted:||2022-10-05 14:11|
|Submitted by:||Zhou, Zheng|
|Submitted to:||SciPost Physics|
Incommensurability plays a critical role in many strongly correlated systems. In some cases, the origin of such exotic order can be theoretically understood in the framework of 1d line-like topological excitations known as ``quantum strings''. Here we study an extended transverse field Ising model on a triangular lattice. Using the large-scale quantum Monte Carlo simulations, we find that the spatial anisotropy can stabilize an incommensurate phase out of the commensurate clock order. Our results for the structure factor and the string density exhibit a linear relationship between incommensurate ordering wave vector and the density of quantum strings, which is reminiscent of hole density in under-doped cuprate superconductors. When introducing the next-nearest-neighbour interaction, we observe a quantum tricritical point out of the incommensurate phase. After carefully analyzing the ground state energies within different string topological sectors, we conclude that this tricriticality is non-trivially caused by effective long-range inter-string interactions with two competing terms following different decaying behaviours.
Author comments upon resubmission
We appreciate the positive evaluation of both Referees that `the paper is scientifically sound and well written' and `the problem is interesting and the results are intriguing'. We also thank their critical comments that are important to understanding the problems in concern. These points have all been properly addressed in the attached reply.
Thanks to the comments of the Referees, we have made substantial improvements to the paper. The revisions made are listed above.
We give a point-by-point response to the comments of all Referees. We believe that the changes made have improved our paper and hope that the current manuscript will be considered suitable for further consideration in SciPost Physics.
List of changes
1. To address the concern on the possible phases at $J_x<J$ (Comment 1 of Referee 1), we have stressed that the discussion in Section 2, Paragraph 2 only applies to the classical Ising limit $h=0$.
2. To address the concern on the meaning of the word `vibration' of the string (Comment 3 of Referee 2), we have added reference to related illustration in Section 2, Paragraph 5.
3. To address the question on the stripe phase (Comment 2 of Referee 2), we have added a related brief discussion to Section 3, Paragraph 2.
4. To address the concern on the width of incommensurate plateaux (Comment 5 of Referee 2), we have added a sentence to stress the finite size scaling result in Section 3, Paragraph 6.
5. To address the concern on the ansatz of the effective inter-string interaction (Comment 3 of Referee 1, and Comment 4 of Referee 2), we have added a detailed discussion in Section 4, Paragraph 5 and revised the wording in the Abstract and Conclusion.
6. To address the concern on the leading order approximation of $B$ (Comment 2 of Referee 1), we have appended a discussion in Section 4, Paragraph 7.
Submission & Refereeing History
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Reports on this Submission
Anonymous Report 2 on 2022-10-14 (Invited Report)
1.) Interesting relevant model for frustration and criticality
2.) Groundbreaking analytic analysis in terms of interacting strings
3.) Convincing large scale QMC simulations
1.) some discussions are missing or not detailed enough (see report)
The authors consider the transverse field Ising model on a triangular lattice,
which is an interesting model for rich critical behavior due to the interplay
of frustration and quantum effects. By considering an anisotropic coupling
it is possible to explain much of the behavior with an effective description in
terms of interacting strings, which is supported by large scale numerical simulations.
Apart from the necessary changes (below), I find the paper truly convincing. The work
meets the acceptance criteria and should be published after those changes have
1.) In the description of the construction of strings on page 4, I could not understand
the following sentence: "To avoid creation of triangle-rule-breaking defects (also known as
spinon topological defects), each bisector within the string can only choose left-going
or rightgoing directions" What is meant by "bisector"? Where do I see the directions in
Fig 2? I recommend that the explanation is expanded in more detail.
2.) In Eqs. (2) the energy of the quantum strings are defined. It should be
explained if there is a kinetic energy as well or why it can be neglected.
3.) In Eq. (5) the string density is defined, which appears to be quantized
in the numerical simulations. Is it a conserved quantity or is there another
explanation for this discrete behavior (finite size effect)? The change of the
peak position is argued to become continuous in the thermodynamic limit, but does
(density x length) remain quantized?
4.) The assumption of a power law interaction in Eq. (9) is not rigorously motivated
as previous referees also commented.
A discussion would be useful how important this assumed form is to the final outcome,
or if other forms of two competing interactions have also been tried. The clear evidence
of a long range attractive contribution to the interaction is surprising and interesting.
What could be the mechanism? The newly inserted paragraph does not explain why
one part is attractive.
5.) The relation to the hard-core boson model in Ref.  should be discussed
in more detail, which seems to follow similar physics. What is different?
Is the universal critical behavior the same?
6.) Editorial changes: Refs.  and  are identical.
Please check for spelling mistakes ("incommensurte"on p.2)
and spurious articles (remove "the" in front of QMC simulations).
Anonymous Report 1 on 2022-10-6 (Invited Report)
The authors have properly addressed the comments and questions I raised in the previous report. Now, I would recommend the paper for publication in the present form.