SciPost Submission Page
Pair binding and Hund's rule breaking in high-symmetry fullerenes
by R. Rausch, C. Karrasch
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Christoph Karrasch · Roman Rausch |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2505.21455v2 (pdf) |
| Date submitted: | Sept. 23, 2025, 11:35 a.m. |
| Submitted by: | Christoph Karrasch |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Highly-symmetric molecules often exhibit degenerate tight-binding states at the Fermi edge. This typically results in a magnetic ground state if small interactions are introduced in accordance with Hund's rule. In some cases, Hund's rule may be broken, which signals pair binding and goes hand-in-hand with an attractive pair-binding energy. We investigate pair binding and Hund's rule breaking for the Hubbard model on high-symmetry fullerenes C$_{20}$, C$_{28}$, C$_{40}$, and C$_{60}$ by using large-scale density-matrix renormalization group calculations. We exploit the SU(2) spin symmetry, the U(1) charge symmetry, and optionally the Z(N) spatial rotation symmetry of the problem. For C$_{20}$, our results agree well with available exact-diagonalization data, but our approach is numerically much cheaper. We find a Mott transition at $U_c\sim2.2t$, which is much smaller than the previously reported value of $U_c\sim4.1t$ that was extrapolated from a few datapoints. We compute the pair-binding energy for arbitrary values of $U$ and observe that it remains overall repulsive. For larger fullerenes, we are not able to evaluate the pair binding energy with sufficient precision, but we can still investigate Hund's rule breaking. For C$_{28}$, we find that Hund's rule is fulfilled with a magnetic spin-2 ground state that transitions to a spin-1 state at $U_{c,1}\sim5.4t$ before the eventual Mott transition to a spin singlet takes place at $U_{c,2}\sim 11.6t$. For C$_{40}$, Hund's rule is broken in the singlet ground state, but is restored if the system is doped with one electron. Hund's rule is also broken for C$_{60}$, and the doping with two or three electrons results in a minimum-spin state. Our results support an electronic mechanism of superconductivity for C$_{60}$ lattices. We speculate that the high geometric frustration of small fullerenes is detrimental to pair binding.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
We hereby resubmit our manuscript with a major revision that addresses the comments of the referees.
We see that the referees basically give no objections regarding our results, but are mostly curious about the validity of the Hubbard model for the fullerenes. But this seems to miss the point: The aim of the paper is not to argue for the relevance of the Hubbard model for fullerenes, but rather to fill a hole in the knowledge of whether or not it predicts pair binding. The Hubbard model has been studied for fullerenes since the 1990s and there is consensus that it is a valid starting point. In the revised manuscript, we give a brief discussion of the past works, in particular regarding the agreement with the experiment in terms of single-particle spectra. Of course, more complex models (e.g., with long-ranged Coulomb interaction) are expected to have better agreement, but this is always the situation with model systems; and such complexity is best build one step at a time.
We have adjusted the figures and tables in accordance with the requests of the referees and provide the numerical energy values in the appendix. With these changes, we hope for an acceptance of our paper in SciPost.
Referee 2 proposes a downgrading to SciPost Core because correlation functions were not computed, but we argue that this might also miss the point: Correlation functions are irrelevant for the questions we are addressing here. We are after the proof of pair binding, we are not after a deep analysis of the nature of the ground state for the molecules (which in any case will only be true within the Hubbard model).
Best Regards,
Roman Rausch and Christoph Karrasch
List of changes
- added the irrep to Tab. 1
- added Fig. 2.
- added error bars to the figures
- optical changes to the figures (e.g., aspect ratio)
- expanded on the DMRG method (now App. B)
- documented raw data (App. C)
- added a discussion of the relevance of the Hubbard model
- changes to the wording (see replies to the referees)
Current status:
Reports on this Submission
Report
Recommendation
Accept in alternative Journal (see Report)
Strengths
Weaknesses
Report
However, I am still not convinced about the apparently central scientific point, the violation of Hund's rule in electron-doped $C_{60}$. If clearly evidenced, this would serve as a proxy for an electronic pairing mechanism that may underlie superconductivity in alkali-fullerene compounds. This would've been quite a remarkable result and indeed, this appears to be the authors' "selling point" for publication in SciPost. However, as it's now clear in Fig. 9, the ordering of the different spin sectors is quite ambiguous for 63 and 64 electrons, and it's unlikely this would improve without much larger-scale (or otherwise improved) simulations.
I'm also unhappy that the authors paid little attention to the other referee's suggestion to consider correlation functions. While DMRG energies may be hard to push beyond what's in the paper, correlation functions could've given the authors an alternative way to find more solid evidence for electronic pairing and enhance the significance of their paper.
The technical aspects of the paper are still quite impressive, but I do not think they warrant publication in SciPost Physics on their own. Without an unambiguous physical result with potential relevance for fullerene superconductors, I believe the paper is more suitable for SciPost Physics Core.
Requested changes
1- Re my earlier question on Eq. (1): $E_b$ obviously depends on $N_{tot}$ and in any given compound, there should be a particular value that is relevant. It's not always clear what this value is in the graphs and otherwise. For example, what is it in Fig. 4? Based on Fig. 3, I'd guess it's $E_{20}+E_{22}-2E_{21}$, which doesn't sound like the "half-filled ground state". Wouldn't $E_{19}+E_{21}-2E_{20}$ make more sense? This should be clarified in the text for $C_{20}$ and maybe comment on what $N_{tot}$ is really relevant for $C_{60}$.
2- In Fig. 9, middle panel, the circles around the extrapolated values cover the serifs of the error bars. A symbol that marks the extrapolated value itself (like a cross or a third serif in the middle) might be more useful for the other plots too?
Recommendation
Accept in alternative Journal (see Report)
Author: Roman Rausch on 2025-10-17 [id 5941]
(in reply to Report 1 on 2025-10-14)Comment:
We did address the request for correlation functions, but the referees didn't counter-address it. Long-range pairing correlations *on the molecular lattice* would provide evidence for electronic pairing, but this problem is intractable. The energies of a single molecule serve as proxy quantity for pairing on the lattice (as we explain in the introduction), but we can't think of a intra-molecular correlation function that would enhance this evidence; and there has been no explicit suggestion by the referees.
Furthermore, energies generally converge faster than correlation functions in DMRG, and so provide the highest-quality data.
Finally, this request would require repeating numerical calculations that take weeks to months to complete.