SciPost Submission Page
Precision magnetometry exploiting excited state quantum phase transitions
by Qian Wang, Ugo Marzolino
Submission summary
Authors (as registered SciPost users):  Ugo Marzolino 
Submission information  

Preprint Link:  https://arxiv.org/abs/2306.01126v5 (pdf) 
Date accepted:  20240723 
Date submitted:  20240708 12:13 
Submitted by:  Marzolino, Ugo 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
Critical behaviour in phase transitions is a resource for enhanced precision metrology. The reason is that the function, known as Fisher information, is superextensive at critical points, and, at the same time, quantifies performances of metrological protocols. Therefore, preparing metrological probes at phase transitions provides enhanced precision in measuring the transition control parameter. We focus on the LipkinMeshkovGlick model that exhibits excited state quantum phase transitions at different magnetic fields. Resting on the model spectral properties, we show broad peaks of the Fisher information, and propose efficient schemes for precision magnetometry. The LipkinMeshkovGlick model was first introduced for superconductivity and for nuclear systems, and recently realised in several condensed matter platforms. The above metrological schemes can be also exploited to measure microscopic properties of systems able to simulate the LipkinMeshkovGlick model.
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 multipronged followup work
 Detail a groundbreaking theoretical/experimental/computational discovery
 Present a breakthrough on a previouslyidentified and longstanding research stumbling block
Author comments upon resubmission
we understand the referee's issue, and therefore we have amended the claims according to the referee's suggestions. We also drawn new plots as suggested by the referee. The plot of $F/N^2$ requested in the report is the new figure 11. In the report attachment, the referee also asks for the plot of $\mathcal{F}_{h,m}/N^2$ instead of $\mathcal{F}_{h,m}$ in figure 4. We guess the referee meant $\mathcal{F}_{h,m}^*$ as this is the quantity plotted in figure 4. $\mathcal{F}_{h,m}^*$ in figure 4 (as well as $\mathcal{F}_{h,m}$ in figure 3) is plotted as a function of $N$ in loglog scale: there are not curves $\mathcal{F}_{h,m}^*$ and $\mathcal{F}_{h,m}$ for different $N$. The plot for $\mathcal{F}_{h,m}^*/N^2$ similar to that in figure 4 is simply the same as $\mathcal{F}_{h,m}^*$ with slope $\xi2$ instead of $\xi$. We therefore plotted $\mathcal{F}_{h,m}^*/N^2$ as function of $h$ and $\mathcal{F}_{h,m}/N^2$ as function of the eigenenergy for different $N$ in figure 12. Notice that $\mathcal{F}_{h,m}$ is the maximum of $\mathcal{F}_h$ over all $h$ (the peak value exemplified in figures 2(a) that corresponds to fixing $h=h_c^k$), then it depends only on the eigenenergy and on $N$. Similarly, $\mathcal{F}_{h,m}^*$ is the maximum of $\mathcal{F}_h$ over all eigenenergies (the peak value exemplified in figures 4(a,b) with $E_k=E_c$), then it depends only on $h$ and on $N$.
Figures 11 and 12 show that $\mathcal{F}_h/N^2$ overlap for different $N$ except around the peak, whose value slowly increases with $N$. This is compatible with the fit of the peak values $\mathcal{F}_{h,m}$ and $\mathcal{F}_{h,m}^*$ which show a power law with exponent slightly larger than $2$. We do not enter the question whether these scalings are signature of the excited state quantum phase transition, as this is not the scope of our manuscript. Moreover, we do not think that this discussion is fundamental for presenting out results in the field of quantum metrology, as already acknowledged by the referee. For these reasons and in order to not weight down the main discussion, we commented on the new figures in appendix B and we amended the claims as suggested by the referee.
We think that we have addressed the criticisms of the referee, and that the new resubmitted manuscript is suitable for publication.
Yours sincerely,
Qian Wang and Ugo Marzolino
List of changes
\begin{itemize}
\item The sentence "$\mathcal{F}_h$ exhibits a sharp peak close to the critical energy $E_c$, and its maximum value [...] increases with the system size $N$" has been replace by "$\mathcal{F}_h$ exhibits a sharp peak close to the critical energy $E_c$ [...]", dropping the reference to the size scaling, and we have consistely reworded the beginning of the next sentence.
\item The sentence "We suggest that the superextensive peaks of the QFI [...] are a signature of the ESQPT" has been removed, and we have consistely reworded the beginning of the paragraph.
\item We have changed the title of appendix B, and discussed the new figures 11 and 12 there.
\end{itemize}
Current status:
Editorial decision:
For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)
Reports on this Submission
Report
The authors have modified the manuscript following my recommendations. In particular, the new Fig.11 seems to confirm the point, I made, ie, that the superextensive scaling observed here is a property of the QFI for higherexcited state, but is not directly related to the presence of an ESQPT.
I still believe that the origin of the superextensive scaling observed here is an important issue which has not been fully adressed in the manuscript, and I think it would have been more transparent to put the new Fig.11 in the main text, instead of relegated in an Appendix. However, given the changes that have already been made, and in order not to drag things down too long, I recommand publication of the manuscript as it stands.
Recommendation
Publish (meets expectations and criteria for this Journal)