SciPost Submission Page
Downfolding the Su-Schrieffer-Heeger model
by Arne Schobert, Jan Berges, Tim Wehling, Erik van Loon
This is not the latest submitted version.
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Jan Berges · Arne Schobert · Erik van Loon |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2104.09207v2 (pdf) |
| Date submitted: | 2021-05-11 11:07 |
| Submitted by: | van Loon, Erik |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
Charge-density waves are responsible for symmetry-breaking displacements of atoms and concomitant changes in the electronic structure. Linear response theories, in particular density-functional perturbation theory, provide a way to study the effect of displacements on both the total energy and the electronic structure based on a single ab initio calculation. In downfolding approaches, the electronic system is reduced to a smaller number of bands, allowing for the incorporation of additional correlation and environmental effects on these bands. However, the physical contents of this downfolded model and its potential limitations are not always obvious. Here, we study the potential-energy landscape and electronic structure of the Su-Schrieffer-Heeger (SSH) model, where all relevant quantities can be evaluated analytically. We compare the exact results at arbitrary displacement with diagrammatic perturbation theory both in the full model and in a downfolded effective single-band model, which gives an instructive insight into the properties of downfolding. An exact reconstruction of the potential-energy landscape is possible in a downfolded model, which requires a dynamical electron-biphonon interaction. The dispersion of the bands upon atomic displacement is also found correctly, where the downfolded model by construction only captures spectral weight in the target space. In the SSH model, the electron-phonon coupling mechanism involves exclusively hybridization between the low- and high-energy bands and this limits the computational efficiency gain of downfolded models.
Current status:
Reports on this Submission
Report #1 by Matthieu Verstraete (Referee 1) on 2021-6-13 (Invited Report)
- Cite as: Matthieu Verstraete, Report on arXiv:2104.09207v2, delivered 2021-06-12, doi: 10.21468/SciPost.Report.3054
Strengths
1 - the manuscript deals with an interesting and unexplored issue in the quality of downloading methods for treating electron phonon coupled problems.
2 - the analysis is very in depth and complete, given the simplicity of the SSH interactions
3 - the perturbation theory treatment is transparent, identifying orders of expansion and fully analytical expressions for self energies and effective coupling parameters
4 - novel features are brought to light, such as higher orders of phonon contribution to the effective EPI, and the distinction between spectral weight and orbital mixing effects.
Weaknesses
1 - the model's simplicity (few bands, no competing anharmonicity) are an advantage in the analysis, but it is not trivial to determine which aspects of the treatment will carry over to full ab initio downfolding calculations
2 - the full parameter space of the SSH model is not explored, only the dimerization transition. It could be that some of the derivations actually carry over to the whole space, I have little feeling for this.
Report
Comments:
The SSH model is presented as targeted for CDW transitions : there are additional ingredients in the full treatment of the CDW, in particular more complex (or purely electronic) screening effects, nesting etc... There is a (sometimes sterile) debate in the literature about the nature of CDWs (purely electronic, always with a phonon contribution, with or without nesting...).
The present authors equate CDW with Peierls and with an explicit electron phonon mechanism, but in principle CDW could arise from purely electronic instabilities which give broken translation symmetry at equilibrium ionic positions. I think it would be useful to give some context for this and recognize there are CDW cases and mechanisms which may be completely outside the SSH type of mechanism.
What happens at finite T? The electron hole symmetry might be broken, but the Green's function treatment and other derivations should be easy to transpose.
In Sect 4 the first derivative coupling is cited, and indeed is 99% of the literature, but in advanced theories (e.g. Allen Heine Cardona) second order terms can appear as well for the Fan and Debye Waller contributions to the self energy.
I do not quite understand the phrase before Eq 18 "e.g. at order alpha^2". In principle self energies can contain arbitrarily high order diagrams...
A reference is missing for Hirsch Fye QMC, though this is incidental.
Requested changes
I would appreciate some more comment on the general applicability of the different conclusions of the paper. Is the appearance of 2 phonon diagrams in the downlfolded interaction generic? It seems to depend only on +- alpha symmetry, but it could necessitate also a very simple band structure or a 1D dynamics etc...
And the reasoning about orbital mixing out of the target space is insinuated to be general, but a stronger statement might be made. Do the authors suggest a criterion for choosing the best target space in a full ab initio calculation? (adding a few bands which might mix in, for instance)
The dimerization transition is enforced explicitly. Could the authors
1 - provide an overview of other known phases of the SSH model?
2 - make a statement about which aspects of the calculations will carry over to other phonon modes, band structures etc...?
3 - comment on the relation between the induced anharmonicity and one that would be present in the original system? Will they just sum or somehow interfere?
typos etc:
bottom of p.2: "despite the unquestionable"
fig 2: the x axis labels overlap with the caption