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A higher-order topological twist on cold-atom SO($5$) Dirac fields
by Alejandro Bermudez, Daniel González-Cuadra, Simon Hands
This is not the latest submitted version.
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Alejandro Bermudez |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202310_00005v2 (pdf) |
| Date submitted: | 2024-03-27 11:00 |
| Submitted by: | Bermudez, Alejandro |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
ed as a flexible quantum simulator of Dirac quantum field theories (QFTs) that combine Gross-Neveu and Thirring interactions with a higher-order topological twist. We show that the lattice model corresponds to a regularization of this QFT with an anisotropic twisted Wilson mass. This allows us to access higher-order topological states protected by a {discrete SO($5$) group}, a remnant of the {continuous} rotational symmetry of the 4-Fermi interactions that is not explicitly broken by the lattice discretization. Using large-$N$ methods, we show that the 4-Fermi interactions lead to a rich phase diagram with various competing fermion condensates. Our work opens a route for the implementation of correlated higher-order topological states with tunable interactions that has interesting connections to non-trivial relativistic QFTs of Dirac fermions in $D=2+1$ dimensions.
List of changes
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- We have corrected several typos spotted by the 1st Referee (red in the marked pdf).
- Following the suggestion of the 2nd Referee, we have checked the grammar and corrected additional typos (red in the marked pdf)
- Following the suggestion of the 1st Referee, we have avoided using the adjective ‘hidden’ when referring to the SO(5) protecting symmetry, and used instead ‘discrete SO(5) rotation’, emphasizing that this describes the invariance of the model under a discrete subgroup of SO(5).
- We have corrected the mistake regarding the connection to the AIII class versus the BDI class at several places of the manuscript (see red changes in the market manuscript)
- We have included a new subsection IV.C to discuss the detection in ultra cold atomic gases, and the possibility of inducing sharp boundaries with optical potentials.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 1) on 2024-4-8 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202310_00005v2, delivered 2024-04-08, doi: 10.21468/SciPost.Report.8848
Strengths
The results presented are interesting and relevant for both the study of HOTIs and quantum simulations of field theories.
Weaknesses
The discussion on the experimental protocols to detect the non-trivial phases of the addressed systems is weak and generic.
Report
The authors improved the clarity of their exposition.
However, I ask a further effort to extend Sec. IVC which, in my opinion, is not yet sufficient to convey a realistic idea about the observation of the boundary modes. Using the authors' words, I may say that I am not satisfied by the "middle ground" they have chosen.
In particular, the authors mention that "localized boundary modes, such as corner modes, can be directly detected in real space by locally resolving the atomic density using a quantum gas microscope". However, a straightforward use of a quantum gas microscope (applied to the ground state of the fermionic system) would not distinguish in general the contribution of bulk, edge or corner modes, and would return the overall density resulting from all these contributions.
How can the local density discriminate between the trivial and HOTI phases? Is there a difference in the corner density one expects in the two phases for sharp boundaries? Can the authors specify more explicitly whether this happens in a specific limit, or, in general, there is a discontinuity at the phase transition? Is there a way of doing spectroscopy to obtain a local density of states?
Or are the authors thinking about some specific out-of-equilibrium protocol as in Ref. 207?
Also the comment on the entanglement spectrum is too vague. Ref. 210 concerns ions used as qubits, and not atoms. And I tend to think that the density matrices that one has to calculate to obtain indications about the HOTI phases in this ultracold atom setup have almost nothing in common with that work (different physical platform and different basis: in the HOTI I think one has to consider the occupation numbers of the particles, in Ref. 210 it was the inner degrees of freedom of the ions).
In conclusion, I think that the manuscript will be suitable for publication in SCIPOST Physics only after the authors extend Sec. IVC by outlining physical protocols for the detection of the HOTI phases in a more detailed and rigorous way.
Additional minor remarks:
In this webpage, the first line of the abstract is incomplete. The manuscript is correct.
In page two " ‘discrete SO(5) rotation " -> " ‘discrete SO(5) rotation' "
Concerning the notation "t" used for both time and the tunneling, I still find that not all the issues have been solved. "t" is introduced as a tunneling amplitude in Eq. 12. However, in the exponents of Eqs. 25 and 26, "t" is still labelling the time. I ask the authors a further effort to avoid this ambiguity in the notation.
Requested changes
Extension of Sec. IVC in a more rigorous and detailed form.
Report #1 by Anonymous (Referee 2) on 2024-4-5 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202310_00005v2, delivered 2024-04-05, doi: 10.21468/SciPost.Report.8833
Report
I am happy with the changes made and would like to recommend this paper for publication.
Author: Alejandro Bermudez on 2024-05-10 [id 4481]
(in reply to Report 1 on 2024-04-05)
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% Resubmission of “A higher-order topological twist on cold-atom SO(5) Dirac fields”
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We would like to thank the Referee for assessing our first resubmission, and for considering that the changes performed sufficed to merit publication in SciPost.
Sincerely yours,
The authors
Author: Alejandro Bermudez on 2024-05-10 [id 4482]
(in reply to Report 2 on 2024-04-08)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Resubmission of “A higher-order topological twist on cold-atom SO(5) Dirac fields”
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We would like to thank the Referee for going through the changes we implemented in our first resubmissions nd for reading critically our new subsection about the possible detection. We are happy to see that the Referee found the majority of the changes performed satisfactory, and that these “improved the clarity of their exposition”.
Regarding the Referee’s concern about detection of topological edge states in cold-atom experiments, we have now extended the “experimental detection” section to make the explanation more detailed. The referee is concerned in particular that the use of a quantum gas microscope “would not distinguish in general the contribution of bulk, edge or corner modes, and would return the overall density resulting from all these contributions.” We think this would not be the case, since the presence of edge/corner states creates an excess of atomic density at the boundaries of the topological phase as compared to the trivial phase. This was indeed measured experimentally in a recent cold-atom experiment where the 1D Haldane phase was realized using a Fermi-Hubbard system [Nature 606, 484–488 (2022)], and the same is true for corner states in 2D [Phys. Rev. B 102, 041126(R) (2020)]. We now mention this explicitly in the manuscript.
Regarding the extraction of the entanglement spectrum, we agree with the referee that the reference we mentioned in our first resubmission addresses trapped-ion systems. We have now updated the reference with a protocol designed to extract the entanglement spectrum in cold-atom systems, which can be done by measuring local densities and currents.
We believe that this section now contains a reasonable discussion of possible detection methods. Even if we agree with the Referee that this could be extended further, even performing numerical simulations to test the ideas for our specific model, this would require a considerable amount of work and go beyond the scope of the manuscript, in our most sincere opinion. We believe that our work already contains several novel results and interesting connections between four-Fermi relativistic lattice field theories and interacting higher-order topological phases, which are independent of possible methods for experimental detection.
The Referee has also noticed a typo and an inconsistency in the use of $t$ for both real time and tunneling strength. We have corrected these two issues in the amended version of the manuscript (see the highlighted red changes)
We would like to thank the Referee for the overall assessment of our work.
Sincerely yours,
The authors
Anonymous on 2024-05-13 [id 4483]
(in reply to Alejandro Bermudez on 2024-05-10 [id 4482])The updated version (v3) of Sec. IVc is more convincing and complete than the previous. I am now convinced that this work provides a genuine contribution to the field, relevant also for future experiments. For these reasons I support its publication in SciPost Physics.