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Dynamics of the order-parameter statistics in the long-range Ising model
by Nishan Ranabhat, Mario Collura
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Submission summary
| Authors (as registered SciPost users): | Mario Collura · Nishan Ranabhat |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202111_00036v1 (pdf) |
| Date submitted: | 2021-11-19 10:38 |
| Submitted by: | Ranabhat, Nishan |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We study the relaxation of the local ferromagnetic order in the transverse field quantum Ising chain with power-law decaying interactions $\sim 1/r^\alpha$. We prepare the system in the GHZ state and study the time evolution of the probability distribution function (PDF) of the order-parameter within a block of $\ell$ when quenching the transverse field. The model is known to support long-range order at finite temperature for $\alpha\leq 2.0$. In this regime, quasi-localized topological magnetic defects are expected to strongly affect the equilibration of the full probability distribution. We highlight different dynamical regimes where gaussification mechanism may be slowed down by confinement and eventually breaks. We further study the PDF dynamics induced by changing the effective dimensionality of the system; we mimic this by quenching the range of the interactions. As a matter of fact, the behavior of the system crucially depends on the value of $\alpha$ governing the unitary evolution.
Current status:
Reports on this Submission
Report #3 by Anonymous (Referee 3) on 2022-1-20 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202111_00036v1, delivered 2022-01-19, doi: 10.21468/SciPost.Report.4206
Report
In this work the authors study the dynamics of the full order-parameter statistics in long-range quantum Ising chains with algebraically decaying interactions. These model systems have become particularly important within the last decade due to experimental developments in certain quantum simulators such as trapped ions which provide a natural realization of these systems. Using a DMRG algorithm based on matrix product states the authors compute the (numerically) exact dynamics of the model in various parameter regimes. They identify two different regimes set by the exponent alpha of the algebraically decaying interactions. For alpha<2 they find that the ferromagnetic order appears (on the considered time scales) stable, which for the initial GHZ state implies an order parameter distribution with two peaks at opposite nonzero magnetization. In the opposite regime, the initial doubly peaked distribution changes fundamentally its character with the two peaks merging over time yielding a simple Gaussian-like form. More specifically, the authors even show more concretely, that such a Gaussianification happens of the distribution.
The manuscript is well written and straightforward to follow also for non-experts in the field. Additionally, the underlying model is of high experimental relevance, and also, in principle, also the calculated order parameter statistics is measurable in experiments (this last point might actually deserve some further discussion). Overall, the discussion of the results for the statistics is more of descriptive form. Although not absolutely necessary I could imagine that a discussion of what kind of additional information the order parameter statistics could provide beyond what is accessible from just looking at the much simpler observables such as the mean value and fluctuations.
Overall, to my impression this manuscript deserves publication in SciPost. Taking into account the aspects mentioned before could, however, be taken into account to further improve the manuscript.
Report #2 by Anonymous (Referee 2) on 2022-1-10 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202111_00036v1, delivered 2022-01-09, doi: 10.21468/SciPost.Report.4163
Strengths
1- Careful numerical study of a challenging problem
2-Well organized and well written results
Weaknesses
1-No theory to understand the data is not developed.
Report
The papers studies the evolution of the probability distribution function (PDF) of the magnetization of a block of spins after a quantum quench in the transverse field Ising chain with long range interactions. In the paper, both a quench of the magnetic field and of the interaction range are studied. The initial state is such that the PDF is non Gaussian. The authors study for which values of parameters the order in the initial state melts, and the PDF becomes Gaussian.
This paper contains interesting numerical findings. The most interesting is perhaps the study of the quench of the interaction range. The PDF itself is an interesting and timely quantity that can also be accessed experimentally. The numerical results are of high quality and are valuable also because the physical system that the authors study is very challenging (an out of equilibrium system with non local interaction and a non standard observable). I am convinced that this paper will be well received. I think, however, that the results would fit better Scipost Physics core, for which I strongly recommend this paper.
Report #1 by Anonymous (Referee 1) on 2022-1-5 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202111_00036v1, delivered 2022-01-05, doi: 10.21468/SciPost.Report.4145
Strengths
- extensive numerical analysis
- interesting physical setting and problem
Weaknesses
- absence of a theory to fully understand numerical results
- low bond dimensions are used without explanation
Report
This paper studies an interesting quantity in an interesting non-equilibrium setting. The model is not integrable and therefore not accessible by theoretical methods. The only solvable points are alpha=0 and alpha=infty. The latter has been theoretically analysed and therefore would be good to compare numerical results at large alpha with the exact results at alpha =infty. The case alpha=0 would be also important to analyse analytically. Finally, it is not clear why chi ~ 100 appears to be enough to study time evolution up to time order 100. Is it a feature of TDVP which conserves total energy? Explanations in this direction would be highly welcomed.
Requested changes
- include analytical data at alpha=infty and compare with numerics
- if possible : include analytical data at alpha=0 and compare with numerics
- comment on the low bond dimensions used