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Long-time divergences in the nonlinear response of gapped one-dimensional many-particle systems
by Michele Fava, Sarang Gopalakrishnan, Romain Vasseur, Siddharth A. Parameswaran, Fabian H. L. Essler
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Fabian Essler |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2411.06167v2 (pdf) |
| Date submitted: | Jan. 27, 2025, 6:33 p.m. |
| Submitted by: | Fabian Essler |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We consider one dimensional many-particle systems that exhibit kinematically protected single-particle excitations over their ground states. We show that momentum and time-resolved 4-point functions of operators that create such excitations diverge linearly in particular time differences. This behaviour can be understood by means of a simple semiclassical analysis based on the kinematics and scattering of wave packets of quasiparticles. We verify that our wave packet analysis correctly predicts the long-time limit of the four-point function in the transverse field Ising model through a form factor expansion. We present evidence in favour of the same behaviour in integrable quantum field theories. In addition, we extend our discussion to experimental protocols where two times of the four-point function coincide, e.g. 2D coherent spectroscopy and pump-probe experiments. Finally, focusing on the Ising model, we discuss subleading corrections that grow as the square root of time differences. We show that the subleading corrections can be correctly accounted for by the same semiclassical analysis, but also taking into account wave packet spreading.
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 multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2025-7-30 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2411.06167v2, delivered 2025-07-30, doi: 10.21468/SciPost.Report.11617
Strengths
1 - precise statement for the result 2 - result entails promising experimental developments for strongly interacting systems 3 - sound derivations
Weaknesses
1 - confuse structure 2 - unclear connection with known literature
Report
The manuscript fully meets the criteria.
I found the work sound and the statement sharp. In general, my main concern regards the structure adopted by the authors, together with the relevance of the wave packet analysis. The work introduces certain linearly divergent terms in higher-order response functions for gapped models with stable quasi-particles, at least in a large enough momentum range. Here, the wave packet approach should play the crucial role of extending the models where the result can be applied, namely by including also non-integrable systems. I found though the analytic derivations by the means of wave packets less transparent and intuitive than the ones for integrable models; moreover, it was also though to link computations in the wave packet framework with those for integrable field theories. For sake of clarity, I would have put the extension by the means of wave packets and semiclassics after all the discussion regarding pump-probe responses in integrable systems, or in a dedicated appendix.
I have some questions regarding different points contained in the manuscript:
- In eq. (3), how is the term $\langle A(q)\rangle_0$ defined?
- "Then the action of the pump potential can be viewed as a quantum quench"; for perturbative quenches (i.e. where $\mu$ is very small) perturbation theory is predicting only in the regime $1/m\ll t \ll \mu^{-1/(2-\Delta)}$ where $\Delta$ is the scaling dimension of the perturbing field (in this case the pump potential). How should I reconcile this result with your statement and your prediction of long-time divergences?
- Across eq. (10) the assumption of splitting the two exponentials between the pump and the probe parts is made. As far as I understand, this is valid only for lowest orders in $\mu$ and $\mu'$. How does this fit with the aim of the paper of investigating higher orders?
- Is there a typo in eq. (60), in the second denominator of the second line $\frac{1}{k_1-k_1}$?
- In eq. (69) you integrate over $r_3$ but there is no variable with that name in the integrand. Is it $r_4$?
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)
Strengths
- very interesting quasiparticle description
- timely and important question
Weaknesses
- not fully clear what are the classes of model displaying the divergence
Report
The only slight modification I would ask is to make more clear what are the types of systems the authors expect these divergences to take place. Clearly quasi particles play an important role, but it would be good to give some explicit example.
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)