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An odd thermodynamic limit for the Loschmidt echo
by Gianpaolo Torre, Vanja Marić, Domagoj Kuić, Fabio Franchini, Salvatore Marco Giampaolo
This is not the current version.
|As Contributors:||Fabio Franchini · Vanja Marić|
|Date submitted:||2021-07-07 17:46|
|Submitted by:||Franchini, Fabio|
|Submitted to:||SciPost Physics|
Is it possible to immediately distinguish a system made by an Avogadro's number of identical elements and one with a single additional one? In this work, we show that a simple 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 typical (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. We employ the prototypical quantum Ising chain to illustrate this phenomenology, which we argue being generic for antiferromagnetic spin chains.
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Anonymous Report 2 on 2021-8-24 (Invited Report)
The results presented in the manuscript are interesting but not surprising. The crux of the paper is the following:
1. Within periodic boundary conditions, whether the antiferromagnetic spin chain is frustrated or not depends on the number of spins (odd/even) in the chain.
2. The energy spectrum of the system is determined by the presence or absence of frustration in the system.
3. The nature of the energy spectrum in turn determines the evolution of the Loschmidt echo (LE) following a local quench which preserves parity but breaks the translational invariance.
Although the results are correct and thorough. In addition to the fact that the results have been demonstrated for a special situation (local quench and Ising system), I do not see the significance or general applicability of the results itself. In particular, the authors argue the importance by highlighting the applicability of the Loschmidt echo in a number of other areas of research, but it is not apparent as to how the sensitivity of the LE to odd/even parity can have any significant impact.
The authors may consider discussing if similar results can be expected for intrinsically frustrated systems (such as the ANNNI model). This would make the results more robust.
In short, I do not recommend the publication of the manuscript in the present form. The manuscript needs to be rewritten addressing the issues mentioned above. Specifically, the impact of the results should be illustrated at least through an example.
The impact of the results should be illustrated at least through an example.
The authors may consider discussing if similar results can be expected for intrinsically frustrated systems (such as the ANNNI model).
Anonymous Report 1 on 2021-8-12 (Invited Report)
The authors investigate even/odd effects in the quench dynamics of
large periodic spin chains using the Loschmidt echo as a probe. They
demonstrate that the dynamical response for systems showing what they
call 'topological frustration' can be markedly different depending
on whether the number of sites in the chain is even or odd. The
example studied is the transverse Ising chain where the quench
consists in modulating the strength of the local transverse field on a
single site, thus breaking translational invariance. The results are
explained both in a qualitative, physical picture and also by
performing a perturbative expansion.
All the obtained results appear solid and the idea of testing such
even-odd effects using a quantum quench and the Loschmidt echo is of
interest. It appears fair to say that this does provide a new
synergetic link to the field of quantum dynamics. The paper in its
current version, in my view, does however not provide an abstract and
introduction which puts the problem into the proper context nor does
it seem to provide citations in a way which is representative and
complete, see below. However, it appears possible to remedy these
issues and an amended manuscript might then be reconsidered for
publication in Scipost Physics.
What I find problematic is the abstract and the introduction. First,
it appears to me that the authors are trying unnecessarily hard to
sell their results. The paper discusses an interesting phenomena but
no foundations will be shaken here as the introduction appears to
imply. Second, the discussion of intensive and extensive thermodynamic
quantities and that those cannot distinguish between "one billion" and
"one billion and one elements" appears to me to be missing the
point. Regular intensive and extensive thermodynamic quantities do
characterize the macrostate of a system. I.e., these are local probes
which cannot distinguish between individual microstates. In contrast,
the Loschmidt echo studied here is a probe of the microstate
itself. For individual quantum states we are actually quite used to
the notion that they can be very sensitive to adding or removing a
single particle or a single site. While these are not to be understood
as exact analogies to the effect studied here, we do understand, for
example, that the removal of a single particle in the X-ray edge
problem leads to the Anderson orthogonality catastrophe or that the
addition or removal of a single site can change the number of edge
modes in a topological insulator and thus drastically alter their
ground-state entanglement properties.
I have two recommendations:
1) To rewrite the abstract and the introduction for the reasons listed above.
2) There is a large literature on the Loschmidt echo for many-body
systems. At least some of this literature seems to be of relevance to
put the results better into context. Just to give one example: here
the authors consider a local quench in the transverse Ising chain. Global
quenches have been considered as well. Is it important that the quench is
local? One could also break translational invariance by having a
staggered, modulated, or small random field component on all sites.