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arxiv: 2505.21455 · v4 · pith:6I73UMSVnew · submitted 2025-05-27 · ❄️ cond-mat.str-el

Pair binding and Hund's rule breaking in high-symmetry fullerenes

R. Rausch , C. Karrasch This is my paper

Pith reviewed 2026-05-22 01:46 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords Hubbard modelfullerenesHund's rulepair bindingdensity matrix renormalization groupMott transitionelectronic superconductivity
0
0 comments X

The pith

Hund's rule breaks in the ground states of C40 and C60 but holds in C28, with pair binding remaining repulsive overall in C20.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper applies large-scale density-matrix renormalization group methods to the Hubbard model on four high-symmetry fullerenes to track how electron repulsion affects spin ordering and pair formation. It shows that C20 stays in a regime where pairs repel each other even after a Mott transition, while C40 and C60 exhibit broken Hund's rule with singlet ground states that become minimum-spin upon light doping. These patterns are presented as evidence that an electronic pairing mechanism can operate in C60-based lattices. A sympathetic reader would care because the findings tie molecular geometry directly to the possibility of superconductivity without phonons.

Core claim

Using the single-orbital Hubbard model, the authors find that Hund's rule is broken for C40 in the neutral singlet ground state but restored upon one-electron doping, while for C60 the rule is broken and doping with two or three electrons yields minimum-spin states; the pair-binding energy in C20 remains repulsive at all studied U, and the Mott transition occurs at U_c approximately 2.2t.

What carries the argument

Density-matrix renormalization group calculations on the Hubbard Hamiltonian that exploit SU(2) spin symmetry, U(1) charge symmetry, and Z(N) rotational symmetry to obtain ground-state spin and pair-binding energies for each fullerene.

If this is right

  • C60 lattices can support superconductivity through an electronic mechanism once doped into the minimum-spin regime.
  • Geometric frustration in smaller fullerenes suppresses pair binding and favors magnetic states up to higher interaction strengths.
  • Hund's rule breaking signals a crossover from magnetic to paired behavior that depends on molecular size and symmetry.
  • Mott transitions occur at molecule-specific values of U/t, with C20 crossing at a lower ratio than earlier estimates.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same symmetry-adapted DMRG approach could be applied to other curved carbon structures to map how curvature and frustration trade off against pairing.
  • If the minimum-spin states survive in extended lattices, they would provide a microscopic route to pairing that is independent of lattice phonons.
  • Testing the model on fullerenes with reduced symmetry would isolate whether high symmetry itself is required for the observed Hund's rule breaking.

Load-bearing premise

The low-energy physics of these fullerenes is captured by a single-orbital Hubbard model containing only on-site repulsion and nearest-neighbor hopping.

What would settle it

A direct measurement or higher-precision calculation showing whether the pair-binding energy in C60 becomes negative at the doping levels where minimum-spin states appear.

Figures

Figures reproduced from arXiv: 2505.21455 by C. Karrasch, R. Rausch.

Figure 1
Figure 1. Figure 1: Schlegel diagrams (nearest-neighbor graphs) of the high-symmetry fullerenes [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Energy levels of the tight-binding (Hückel) model for the high-symmetry [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: DMRG data for the ground-state energy per site for [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Triplet gap Eq. (4) and pair-binding energy Eq. (1) for [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Ground-state energy per site and HOMO filling for [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: (a) The quintet gap Eq. (5) as well as the triplet gap Eq. (4) for [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Ground-state energy per site and HOMO filling for [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Ground-state energy per site for C60 at half filling Ntot = 60 and a total spin Stot = 0 at U = 2. Only data for a SU(2)×U(1)-symmetric calculation is shown (small circles). The bond dimensions are in the range 14 000 ≤ χSU(2) ≤ 16 000. and in [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Ground-state energy per site for C60 at U = 2. Symbols and bond dimensions are as in [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Left: Schlegel diagram of the [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
read the original 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 are consistent with an electronic mechanism of superconductivity for C$_{60}$ lattices. We speculate that the high geometric frustration of small fullerenes is detrimental to pair binding.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates the single-orbital Hubbard model on high-symmetry fullerenes C20, C28, C40, and C60 using large-scale DMRG calculations that exploit SU(2) spin, U(1) charge, and optional Z(N) rotational symmetries. For C20 the results reproduce exact-diagonalization benchmarks, locate a Mott transition at U_c ≈ 2.2t, and show that the pair-binding energy remains repulsive for all U. For the larger molecules, direct pair-binding energies cannot be obtained with sufficient precision, but the authors map Hund's-rule behavior: C28 obeys Hund's rule with a spin-2 ground state that crosses to spin-1 before the Mott transition; C40 breaks Hund's rule in the neutral singlet but restores it upon single-electron doping; C60 breaks Hund's rule and yields minimum-spin states upon two- or three-electron doping. The authors conclude that these findings are consistent with an electronic pairing mechanism for superconductivity in C60 lattices and speculate that geometric frustration suppresses pair binding in smaller fullerenes.

Significance. If the interpretation of Hund's-rule breaking as a proxy for attractive pair binding is valid, the work supplies concrete numerical evidence that interaction-driven pairing tendencies can survive in highly symmetric molecular Hubbard systems, supporting electronic mechanisms proposed for alkali-doped fullerene superconductors. The symmetry-adapted DMRG implementation and its agreement with exact results on C20 constitute clear technical strengths. The inability to compute pair-binding energies directly on C60, however, means the central consistency claim rests on an indirect indicator whose reliability in the relevant parameter window is not independently verified within the manuscript.

major comments (2)
  1. [Abstract] Abstract and concluding discussion: the claim that the C60 results are 'consistent with an electronic mechanism of superconductivity' is grounded in the observation of Hund's-rule breaking and minimum-spin doped states, yet the manuscript states that pair-binding energies cannot be evaluated with sufficient precision for C60 (and larger cages). Because the same DMRG framework finds a repulsive pair-binding energy for all U on C20, an explicit argument is required showing why Hund's-rule violation reliably signals attractive pair binding in the C60 regime; without it the consistency statement remains an untested extrapolation.
  2. [C20 results] C20 results section: the reported Mott transition at U_c ∼ 2.2t is lower than the previously extrapolated value of ∼4.1t. The manuscript indicates that the new value is obtained from finite-bond-dimension or finite-size DMRG data; the extrapolation procedure, bond-dimension scaling, and finite-size corrections used to locate the transition should be documented in detail so that the discrepancy with earlier work can be assessed.
minor comments (2)
  1. [Methods] Notation for the pair-binding energy Δ and the critical interaction strengths U_{c,1}, U_{c,2} should be defined once in the main text and used consistently; occasional redefinition in figure captions creates minor ambiguity.
  2. [Figures] Figure captions for the spin-gap and pair-binding plots should explicitly state the bond dimension and truncation error at which the data were obtained, allowing readers to judge convergence.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address the major comments point by point below.

read point-by-point responses

  1. Referee: [Abstract] Abstract and concluding discussion: the claim that the C60 results are 'consistent with an electronic mechanism of superconductivity' is grounded in the observation of Hund's-rule breaking and minimum-spin doped states, yet the manuscript states that pair-binding energies cannot be evaluated with sufficient precision for C60 (and larger cages). Because the same DMRG framework finds a repulsive pair-binding energy for all U on C20, an explicit argument is required showing why Hund's-rule violation reliably signals attractive pair binding in the C60 regime; without it the consistency statement remains an untested extrapolation.

    Authors: We agree that the connection merits explicit elaboration. The manuscript states that Hund's rule breaking signals pair binding and attractive pair-binding energy. For C20 the pair-binding energy is repulsive for all U, which we attribute to the high geometric frustration of the smallest fullerene as noted in the concluding discussion. For C60 the lower frustration permits Hund's rule breaking in the neutral singlet and minimum-spin states for two- and three-electron doping; this regime is the one relevant to the proposed electronic pairing mechanism in doped C60 solids. We have expanded the discussion section with a paragraph that makes this distinction and the resulting consistency argument explicit. revision: yes

  2. Referee: [C20 results] C20 results section: the reported Mott transition at U_c ∼ 2.2t is lower than the previously extrapolated value of ∼4.1t. The manuscript indicates that the new value is obtained from finite-bond-dimension or finite-size DMRG data; the extrapolation procedure, bond-dimension scaling, and finite-size corrections used to locate the transition should be documented in detail so that the discrepancy with earlier work can be assessed.

    Authors: We agree that a more detailed account of the extrapolation is needed. The lower U_c results from systematic scaling over a wider range of bond dimensions and system sizes than was available in prior work. We have revised the C20 results section to document the bond-dimension scaling of the charge gap, the extrapolation to infinite bond dimension, the finite-size corrections, and the procedure that yields U_c ≈ 2.2t, including additional figures that display the scaling data. revision: yes

Circularity Check

0 steps flagged

No significant circularity: results from direct DMRG on defined Hubbard model

full rationale

All reported quantities (Mott transitions, ground-state spins, pair-binding energies for C20, Hund's rule behavior) are obtained by explicit numerical diagonalization/DMRG of the single-orbital Hubbard Hamiltonian whose form is stated at the outset. No target observable is defined in terms of a fitted parameter that is subsequently re-derived from the same data. The abstract's general statement that Hund's rule breaking signals pair binding is presented as a known association rather than a self-referential derivation; for C60 the paper explicitly notes the inability to compute pair-binding energy directly and instead reports the observed minimum-spin states. No load-bearing self-citation chain or ansatz smuggling appears in the provided text. The derivation chain is therefore self-contained against the numerical benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claims rest on the standard Hubbard-model approximation for pi-electrons in fullerenes and on the numerical convergence of DMRG; no new particles or forces are introduced and the only adjustable parameter is the ratio U/t which is scanned rather than fitted to a target observable.

free parameters (1)
  • U/t ratio
    Interaction strength is varied continuously to locate critical points; the reported Uc values are outputs of the scan rather than inputs.
axioms (1)
  • domain assumption Low-energy physics of these fullerenes is captured by a single-band Hubbard model with nearest-neighbor hopping t and on-site repulsion U only.
    Invoked when the Hamiltonian is defined for C20, C28, C40, and C60 in the opening paragraphs of the methods.

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Reference graph

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