# Time-dependent variational Monte Carlo study of the dynamic response of bosons in an optical lattice

### Submission summary

 As Contributors: Mathias Gartner · Ferran Mazzanti · Robert Zillich Arxiv Link: https://arxiv.org/abs/2202.07535v2 (pdf) Date accepted: 2022-06-14 Date submitted: 2022-05-30 13:11 Submitted by: Gartner, Mathias Submitted to: SciPost Physics Academic field: Physics Specialties: Atomic, Molecular and Optical Physics - Theory Approaches: Theoretical, Computational

### Abstract

We study the dynamics of a one-dimensional Bose gas at unit filling in both shallow and deep optical lattices and obtain the dynamic structure factor ${S(k,\omega)}$ by monitoring the linear response to a weak probe pulse. We introduce a new procedure, based on the time-dependent variational Monte Carlo method (tVMC), which allows to evolve the system in real time, using as a variational model a Jastrow-Feenberg wave function that includes pair correlations. Comparison with exact diagonalization results of ${S(k,\omega)}$ obtained on a lattice in the Bose-Hubbard limit shows good agreement of the dispersion relation for sufficiently deep optical lattices, while for shallow lattices we observe the influence of higher Bloch bands. We also investigate non-linear response to strong pulses. From the power spectrum of the density fluctuations we obtain the excitation spectrum, albeit broadened, by higher harmonic generation after a strong pulse with a single low wave number. As a remarkable feature of our simulations we furthermore demonstrate that the full excitation spectrum can be retrieved from the power spectrum of the density fluctuations due to the stochastic noise inherent in any Monte Carlo method, without applying an actual perturbation.

###### Current status:
Publication decision taken: accept

Editorial decision: For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)

Dear Editor,

Please find our resubmission of the manuscript which includes the suggestions raised by the referees. We hope that they are adequate and suitable to warrant publication in the SciPost Physics journal.
The answers to the referees' questions can be found as comments to the reports.

Yours sincerely,
Mathias Gartner, Ferran Mazzanti and Robert E. Zillich

### List of changes

Taking into account the referees’ suggestions, we made the following changes to the manuscript:
- change the title to “Time-dependent variational Monte Carlo study of the dynamic response of bosons in an optical lattice”
- dividing the manuscript in sections
- corrected the expression for the local energy $E=H \Psi / \Psi$ [Report 2.4]
- in abstract distinguish between the power spectrum of density fluctuations and the dynamic structure factor [Report 1.1]
- we now refer to $|\delta \tilde \rho (k, \omega)|$ as the square root of the power spectrum of the density fluctuations
- introduction to our results at the end of the new section “Introduction”
- add explanation why we use the form $sin^2(k_L x)$ as optical lattice potential [Report 2.1]
- add information about the boundary condition on the wavefunction due to the contact interaction [Report 3.2]
- add color legend in Fig. 2 [Report 1.2]
- add more detailed discussion about the comparison with [39] in section 3.1 [Report 1.2]
- in section 3.3 we significantly extend the discussion of the noise in equation (6) [Report 2.2, Report 3.3]
- write the Jastrow ansatz as products of the exponential of correlation functions and extend the description of our variational ansatz for the wavefunction [Report 2.3]
- add new section 2.2 where technical details of the numerical simulations are stated [Report 3]
- we compared the ground state energy of our variational wavefunction for a Lieb Liniger model to Bethe ansatz calculations and state the result in section 3 [Report 3.1]
- correct an error in the $\omega$-axis values in figure 3
- add new references [24], [30], [37] and [38]
- generally we tried to improve readability by changing wording throughout the text
- adding label (a), (b), and (c) for the panels in Fig.3

### Submission & Refereeing History

Resubmission 2202.07535v2 on 30 May 2022
Submission 2202.07535v1 on 1 March 2022

## Reports on this Submission

### Report

I think the the authors addressed all previous concerns and the manuscript is now suitable for publication in SciPost Physics.

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### Report

I thank the authors for clarifying the points I raised in my original reports and for improving the quality of the manuscript. I believe the paper is now ready to be published.

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### Report

I am satisfied with the authors' response to my report and the other reports and recommend publication. The paper meets expectation number 3: it "opens a new pathway in an existing or a new research direction, with clear potential for multipronged follow-up work". It also meets all of the general acceptance criteria.

• validity: -
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