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An odd thermodynamic limit for the Loschmidt echo

by Gianpaolo Torre, Vanja Marić, Domagoj Kuić, Fabio Franchini, Salvatore Marco Giampaolo

Submission summary

As Contributors: Fabio Franchini · Vanja Marić
Arxiv Link: (pdf)
Date accepted: 2022-01-13
Date submitted: 2021-10-06 18:19
Submitted by: Franchini, Fabio
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
  • Statistical and Soft Matter Physics
Approaches: Theoretical, Computational


Is it possible to readily distinguish a system made by an Avogadro's number of identical elements and one with a single additional one? Usually, the answer to this question is negative but, in this work, we show that in antiferromagnetic quantum spin rings a simple out-of-equilibrium experiment can do so, yielding two qualitatively and quantitatively different outcomes depending on whether the system includes an even or an odd number of elements. We consider a local quantum-quench setup and calculate a generating function of the work done, namely, the Loschmidt echo, showing that it displays different features depending on the presence or absence of topological frustration, which is triggered by the even/oddness in the number of the chain sites. We employ the prototypical quantum Ising chain to illustrate this phenomenology, which we argue being generic for antiferromagnetic spin chains, as it stems primarily from the different low energy spectra of frustrated and non frustrated chains. Our results thus prove that these well-known spectral differences lead indeed to distinct observable characteristics and open the way to harvest them in quantum thermodynamics protocols.

Current status:
Accepted in other journal; awaiting puboffer acceptance

Editorial decision: For Journal SciPost Physics Core: Publish
(status: Awaiting author acceptance of publication offer)

Author comments upon resubmission

We thank the referees and the editor for their work. We appreciate that both referees acknowledge the soundness of our results and we admit that we were probably too carried away by our excitement in the original writing of the manuscript. We felt that the fact that we finally found a way to experimentally detect the change in the low energy spectral properties of frustrated chains and in this way to distinguish the parity in the chain length was intrinsically cool, and thus we placed admittedly too much emphasis on this aspect and forgot to highlight other reasons of interest.
In this revision we accepted the criticisms from the two reviewers and completely rewrote the introduction and substantially reworked the abstract and conclusion. We strove to better place our work into the vast activity in quantum out-of-equilibrium systems and to keep our excitement in check. We also stressed better the implications of our results (mostly in relation to quantum thermodynamics and energetics), and that, with respect to the dependence of the Loschmidt Echo on the parity of the chain length, our findings are generic for systems featuring only topological frustration (that is, 1D chain in which frustration only arise because of the boundary conditions and in which thus the amount of frustration is not extensive). However, since the LE reflect mostly the different low energy spectra with and without frustration, the two behaviors we feature are qualitatively expect to emerge either in standard gapped systems, or in systems were frustration produces a gapless excitations (as it happens in certain regions of the phase diagram of the ANNNI model, mentioned by one of the referees).
We did not significantly modify the main body of our calculation, but we divided it into sections to help in clarifying the flow of our reasoning and to better separate general considerations from specific examples.
In conclusion, we think we successfully addressed the referee's criticisms and we hope that our paper will now be accepted.

List of changes

We substantially rewrote the paper, completely changing the introduction, but did not introduce new calculations or figure.

Reports on this Submission

Anonymous Report 2 on 2021-11-10 (Invited Report)


The authors have appropriately addressed all the issues. I therefore
recommend the present version of the manuscript for publication.

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Anonymous Report 1 on 2021-10-26 (Invited Report)


I am satisfied with the changes made in response to the reports. The only further comment I have is that the work by

Heyl et al. Physical review letters 110 (13), 135704,

related theoretical work, as well as the experiment

Jurcevic et al. Physical Review Letters 119 (8), 080501

should also be mentioned because those two papers and related theoretical works also deal with the Loschmidt echo after a quantum quench and some of them also consider the transverse Ising model.

As I wrote in my previous report, I believe that this works provides a new connection between topological frustration and quantum dynamics and is therefore of interest for the condensed matter/statistical physics community. I recommend publication in SciPost Physics.

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