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On computing non-equilibrium dynamics following a quench
by Neil J. Robinson, Albertus J. J. M. de Klerk, Jean-Sébastien Caux
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Submission summary
| Authors (as registered SciPost users): | Neil Robinson · Albertus de Klerk |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/1911.11101v3 (pdf) |
| Date submitted: | 2021-02-16 14:05 |
| Submitted by: | de Klerk, Albertus |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Computing the non-equilibrium dynamics that follows a quantum quench is difficult, even in exactly solvable models. Results are often predicated on the ability to compute overlaps between the initial state and eigenstates of the Hamiltonian that governs time evolution. Except for a handful of known cases, it is generically not possible to find these overlaps analytically. Here we develop a numerical approach to preferentially generate the states with high overlaps for a quantum quench starting from the ground state or an excited state of an initial Hamiltonian. We use these preferentially generated states, in combination with a "high overlap states truncation scheme" and a modification of the numerical renormalization group, to compute non-equilibrium dynamics following a quench in the Lieb-Liniger model. The method is non-perturbative, works for reasonable numbers of particles, and applies to both continuum and lattice systems. It can also be easily extended to more complicated scenarios, including those with integrability breaking.
Author comments upon resubmission
List of changes
To address the report of referee 1 we have included the following comment in the conclusions section of the paper.
"Finally, we would like to point out that the method developed in this paper provides, in principle, all the ingredients necessary to compute for example the time evolution of the entanglement entropy. However, the computation of this quantity still represents a significant computational challenge, which we leave for future work. "
Current status:
Reports on this Submission
Report #1 by Anonymous (Referee 3) on 2021-2-24 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1911.11101v3, delivered 2021-02-24, doi: 10.21468/SciPost.Report.2604
Report
I am really surprised by the authors reply that clearly did not read properly my report. I am still very much in favour of publication in SciPost physics, but what the authors wrote in their reply and added to the paper is a complete misunderstanding of my comment.
Calculating ab-initio the entanglement entropy, as the authors write, is so obviously a hopeless task that nobody will dare to do or to mention. I just wrote to use the knowledge of the root density and to plug in the quasiparticles picture formula, to be clear Eq. (4) of the paper https://arxiv.org/pdf/1712.07529.pdf (as one of the many places where this formula can be found). This not only is doable, but it is basically already done in the manuscript.
Requested changes
The authors should remove the comment about the ab-initio evaluation of the entanglement entropy and possibly add one about its quasiparticle determination.
Author: Albertus de Klerk on 2021-09-07 [id 1740]
(in reply to Report 2 on 2021-02-27)We apologize to the referee for misunderstanding their comment and thank the referee for their clarification of the proposed approach.
Approaching the problem of computing the time-evolution of the entanglement entropy using the existing approaches for the thermodynamic limit is indeed an interesting idea, and probably the only viable approach. However, we would like to note that the application of the formula referred to by the referee is strictly only valid after taking the thermodynamic as well as the scaling limit. Therefore, an investigation into the magnitude of finite size effects is warranted in order to understand to what extent the formula mentioned by the referee can be applied to our results. Due to the lengthy nature of our paper, we think that it would be better to leave this direction of investigation to future works.