SciPost logo

SciPost Submission Page

Polaron spectroscopy of interacting Fermi systems: insights from exact diagonalization

by Ivan Amelio, Nathan Goldman

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Ivan Amelio
Submission information
Preprint Link:  (pdf)
Date accepted: 2024-02-09
Date submitted: 2024-01-25 09:28
Submitted by: Amelio, Ivan
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Atomic, Molecular and Optical Physics - Theory
  • Condensed Matter Physics - Theory
Approaches: Theoretical, Computational


Immersing a mobile impurity into a many-body quantum system represents a theoretically intriguing and experimentally effective way of probing its properties.In this work, we study the polaron spectral function in various environments, within the framework of Fermi-Hubbard models. Inspired by possible realizations in cold atoms and semiconductor heterostructures, we consider different configurations for the background Fermi gas, including charge density waves, multiple Fermi seas and pair superfluids. While our calculations are performed using an exact-diagonalization approach, hence limiting our analysis to systems of few interacting Fermi particles, we identify robust spectral features supported by theoretical results. Our work provides a benchmark for computations based on mean-field approaches and reveal surprising features of polaron spectra, inspiring new theoretical investigations.

List of changes

We thank the two Referees for their constructive remarks. Apart from a series of changes in the main text and related plots (that we discussed below), we have performed extensive additional studies, which are now presented in four new Appendices. We believe that this additional material, which nicely supports the main results of our work, constitute a sizable improvement of our manuscript.

Report 1

We thank the Referee for their appreciation of our manuscript and for their useful remarks. We have now added a new Appendix A, which addresses the questions of the Referee about convergence. The bottom line of this analysis is that by comparing different sizes, fillings and lattices it is indeed possible to distinguish the features that would also hold in a thermodynamically large system, from those that are artifacts of finite-size effects.

Regarding the study of Rabi oscillations in this framework: we agree that it may be a very interesting application of our method, and we comment on it in the outlines. However, since this would still require a (conceptually straightforward) rewriting of some parts of our code, and since this does not completely fit the main topic of “interacting fermions”, we have decided to leave it as a future direction.

Report 2

We thank the Referee for their reading of our manuscript and for their useful remarks. In the revised manuscript we adopt a more critical attitude towards the “double line of the attractive polaron branch in a superfluid”. Indeed, while we are inclined to believe that this feature could likely be a finite-size effect, it might still suggest a strong contribution of bosonic, Goldstone-like excitations at energies very close to the AP line (as motivated by the comparison with Appendix D).
We reply point by point to the their questions 1-11:

1) We now explicitly mention the finite-size effect issue: “While
our calculations are performed using an exact-diagonalization approach, hence limiting
our analysis to systems of few interacting Fermi particles, we identify robust spectral
features supported by theoretical results.”.

2) We now discuss this in Appendix A, Fig. 7.c.

3) We now address these issues in Appendix A (finite size corrections) and Appendix B (umklapp peak).

4) First of all, most of the results do not rely on whether the microscopic lattice is chosen to be a square or a triangular one: Indeed, as also pointed out by the Referee, only the band minimum matters.
Following their suggestion, we now mainly display triangular-lattice results in the main text, and moved the square-lattice results to the new Appendix C (showing excellent agreement).

However, we point out that there is a genuine difference between triangular and square lattices in the case of the charge density wave because they give rise to different charge order, with different symmetries. For this reason, we have decided to plot both results in the main text.

Concerning the extra feature in the triangular-lattice results shown in Fig. 3a: We are currently investigating the spectra obtained from a Hartree-Fock approach combined with the Chevy ansatz; while these results will be presented in a future publication, we hereby summarize our current findings: while this Hartree-Fock-Chevy approach can reproduce the main avoided crossing due to the increase of the quasi-particle gap, we find that it does not capture this extra feature. Since larger system sizes are prohibitive, we cannot confirm whether this is a ‘beyond HF+Chevy’ effect or a finite size effect. This limitation is commented in the text.

5) We now explicitly define the +/-K points and use \kappa for the interaction parameter.

6) To reassure the reader, we now added the binding energies in Fig. 4.a, which perfectly match the ED lines. However, as expected, this agreement is only found at small E_F/E_B, since there is a strong redshift due to the Fermi sea at large E_F (this is why we had decided not to plot the binding energy in vacuum in the original version). Notice that this is different from Fig. 5, since in that case it is E_pair that is varied.

7) We now improved the presentation and explicitly provide the relation between the two quantities, U and E_B. The binding energy of the impurity-spin up molecule is still given by Eq. (5), and analogously for the spin down one.
To strengthen and clarify the comparison with the Chevy results, we have now added a new Appendix D, devoted to the BCS+Chevy calculation with the exact same setting as in ED.

8) Now we briefly discuss the main advantages and drawbacks of the cold atom and TMD platforms. Following the Referee’s suggestion, we also point out that our approach is interesting in addressing the question of how the many-body limit is reached starting from few particles and increasing their number.

9) This has now been fixed.

10) We are now more careful when drawing the colorbars of the plots, with proper units 1/E_F.

11) We have fixed all these presentation issues.

We thank once again the Refeere for all their constructive and detailed comments.

Published as SciPost Phys. 16, 056 (2024)

Reports on this Submission

Anonymous Report 2 on 2024-2-5 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2309.07019v2, delivered 2024-02-05, doi: 10.21468/SciPost.Report.8499


I appreciate that the authors took the referees’ comments very seriously. With the careful and detailed modifications in the text and the additional appendices the results are presented in a much more transparent and convincing way.

The first appendix underlines the robustness of the attractive polaron branch with respect to system size. The second appendix nicely illustrates that the umklapp peak only depends on the lattice details, but not on the interaction. Also, I appreciate that the authors now show both results for the triangular and square lattice and give more details on the Chevy ansatz in a BCS superfluid. Generally, the arguments in the paper are much more solid and evident now.

The plots all include colorbars now and the units of the plotted quantities are always provided. I have finally understood the notation with the K-point in the Brillouin zone. Good that the authors now clarify that in the text!

I still have some minor orthographic comments:
- The first sentence on page 14 is not correct: “the lattice just makes *it* technically possible to perform ED”.
- Typos in App. D: “intrduce”, “quasi-particles” vs. “quasiparticles”.
- Inconsistencies of references: “panels (a), (b), (c)” vs. “panels (a-c)”.

The presented analysis with exact diagonalization gives new insights into polaron physics. Above all, I find it rather striking that such small system sizes and the confinement to a lattice reveal typical many-body features. Hence, besides the mentioned trivialities, I recommend the article for publication.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

Anonymous Report 1 on 2024-1-25 (Invited Report)


My questions have been fully answered and I recommend publication as-is.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

Login to report or comment