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Quantum Gutzwiller approach for the two-component Bose-Hubbard model
by V. E. Colussi, F. Caleffi, C. Menotti, A. Recati
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Submission summary
| Authors (as registered SciPost users): | Victor Colussi |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2110.13095v1 (pdf) |
| Date submitted: | 2021-10-29 11:46 |
| Submitted by: | Colussi, Victor |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We study the effects of quantum fluctuations in the two-component Bose-Hubbard model generalizing to mixtures the quantum Gutzwiller approach introduced recently in [Phys. Rev. Research 2, 033276 (2020)]. As a basis for our study, we analyze the mean-field ground-state phase diagram and spectrum of elementary excitations, with particular emphasis on the quantum phase transitions of the model. Within the quantum critical regimes, we address both the superfluid transport properties and the linear response dynamics to density and spin probes of direct experimental relevance. Crucially, we find that quantum fluctuations have a dramatic effect on the drag between the superfluid species of the system, particularly in the vicinity of the paired and antipaired phases absent in the usual one-component Bose-Hubbard model. Additionally, we analyse the contributions of quantum corrections to the one-body coherence and density/spin fluctuations from the perspective of the collective modes of the system, providing results for the few-body correlations in all the regimes of the phase diagram.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2021-12-8 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2110.13095v1, delivered 2021-12-08, doi: 10.21468/SciPost.Report.4015
Weaknesses
I think that the paper is extremely long and detailed and is not easy to read.
Report
In this work, Colussi and coworkers analyze the two-component Bose-Hubbard model by using the Gutzwiller approach. In particular, they focus the attention on the ground-state phase diagram and the the low-energy spectrum. The results are interesting for the community working on cold atoms. The paper is rather detailed and long and, therefore, not easy to follow. In particular, it looks that the results are listed one after the other, without an explanation on their actual relevance and connection to what has been already seen. For example, I do not understand the actual motivation of the section on the correlation functions, since it does not add much on what we learned from section 3. In this sense, it would be useful to add a motivation to study correlation functions, beyond what has been already done.
Minor points:
1) In Fig.1, it would be useful to see in panels a) and b) what is the curve mu=mu(U) corresponding to the curves reported in panels c), d) and e) (the latest one is not described in the caption).
2) In Fig.7, the panels could be taken a bit wider than now.
3) In Fig.8, the caption is not compatible with the positions of the panels.
In summary, I think that the paper is nice and could be published after my remarks will be addressed.
Report #1 by Anonymous (Referee 1) on 2021-12-6 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2110.13095v1, delivered 2021-12-06, doi: 10.21468/SciPost.Report.4004
Report
In this manuscript the authors explore the phase diagram of the two components Bose-Hubbard
model, focusing on the study of phase transitions between the Mott insulating phase and several
superfluid phases, using the Quantum Gutzwiller formalism, both for the ground state and using
linear response theory. The description of the physical problem is clear and the Quantum Gutzwiller theory (along with the computation strategy) is explained in a very detailed way, with extended
clarifications given in the appendices.
The shown results provide an extension and generalization of the ones obtained for the one species Bose Hubbard model, and comparisons with Quantum Monte Carlo simulations and the predictios of the mean field theory are discussed.
I find that the work is original, and that the methodology used and the results obtained are high
quality and of interest for the ultra cold quantum gases community; I think however that a couple
of clarifications are needed.
In the discussion of the collisionless drag in the superfluid regime (Section 3.2.1) a comparison with Quantum Monte Carlo results is shown. In particular it is stated that the QGW results are within the statistical uncertainty from the QMC data. However in Figure 9 error bars on the QMC data are
neither shown nor mentioned. Can this point be further elaborated?
In section 3.2.2 in the discussion of the Mott Insulator to Superfluid it is stated that the superfluid
density is always larger than the condensate fraction $\vert \psi_{0,i}\vert^2$. Can the comparison between
superfluid density and condensate fraction be more explicitly shown, either in the plot in Figure 10, or by providing some numerical values?
A few additional remarks, regarding the figures:
* In the caption of Fig.1 there is some confusion with the labels (panel d actually refers fo MI/SF
transition and panel e to the CFSF/SF one).
* In Fig.2 I think it should be more explicit that the blue dotted line refers to the non dispersive
modes (it is stated in the body of the text, but I think that it would be clearer if it was mentioned in
the caption too)
* Looking at the caption and the labels referring to sound velocities/response functions it looks to me that the upper/lower panels in Figure 8 are swapped.