# The antiferromagnetic $S=1/2$ Heisenberg model on the C$_{60}$ fullerene geometry

### Submission summary

 As Contributors: Matthias Peschke · Cassian Plorin · Roman Rausch Preprint link: scipost_202011_00015v2 Date accepted: 2021-03-31 Date submitted: 2021-02-12 15:28 Submitted by: Rausch, Roman Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory Condensed Matter Physics - Computational Approaches: Theoretical, Computational

### Abstract

We solve the quantum-mechanical antiferromagnetic Heisenberg model with spins positioned on vertices of the truncated icosahedron using the density-matrix renormalization group (DMRG). This describes magnetic properties of the undoped C$_{60}$ fullerene at half filling in the limit of strong on-site interaction $U$. We calculate the ground state and correlation functions for all possible distances, the lowest singlet and triplet excited states, as well as thermodynamic properties, namely the specific heat and spin susceptibility. We find that unlike smaller C$_{20}$ or C$_{32}$ that are solvable by exact diagonalization, the lowest excited state is a triplet rather than a singlet, indicating a reduced frustration due to the presence of many hexagon faces and the separation of the pentagonal faces, similar to what is found for the truncated tetrahedron. This implies that frustration may be tuneable within the fullerenes by changing their size. The spin-spin correlations are much stronger along the hexagon bonds and exponentially decrease with distance, so that the molecule is large enough not to be correlated across its whole extent. The specific heat shows a high-temperature peak and a low-temperature shoulder reminiscent of the kagomé lattice, while the spin susceptibility shows a single broad peak and is very close to the one of C$_{20}$.

Published as SciPost Phys. 10, 087 (2021)

We would like to thank all the referees for their constructive criticism. We could not do it justice by just changing a sentence here and there, but had to rewrite large parts of the text, update several figures and perform additional calculations.

### List of changes

- improvements of formulations in accordance to the referees' remarks throughout the manuscript
- corrected typos and notations throughout the manuscript
- inclusion of Ref. 13 and its mention in Sec. 1
- comparison with the Cairo tiling (Ref. 22) in Sec. 1
- mention of the icosidodecahedron and the truncated tetrahedron (C12) in Sec. 1
- discussion of the mapping to the chain in Sec. 2.1
- inclusion of C12 and the icosidodecahedron into Sec. 2.2
- inclusion of the quintet gap into Tab. 1
- shortening of the discussion of the distance dependence of the correlation functions in Sec. 2.3
- comparison with the icosidodecahedron and C12 in Sec. 2.3
- clearer formulation of the significance of the n to infinity limit at the end of Sec. 2.3
- addition of Tab. 2 (gaps for various polyhedra)
- the numbering of the sites is now shown in Fig. 4
- Fig. 5 now contains the icosidodecahedron and C12 instead of the icosahedron
- Fig. 5 now contains the exponential fit of the distance dependence in the inset
- more thorough discussion of the irreducible representations in Sec. 3
- comparison to the icosidodecahedron in Sec. 3
- more detailed discussion of the TDVP approach in Sec. 4.1
- the parameters used in the finite-temperature calculations are presented in Tab. 3
- comparison with the icosidodecahedron and C12 in the discussion of the specific heat (Sec. 4.2)
- better comparsion to the kagome lattice in Sec. 4.2, mentioning of the possibility of a gapless state, inclusion of the icosidodecahedron
- the quintet gap and 0.417*triplet gap are shown in Fig. 8
- icosahedron exchanged for C12 in Fig. 8
- icosahedron exchanged for C12 in Fig. 9
- clearer conclusion regarding the questions of frustration vs. order in Sec. 5
- final comparison with the icosidodecahedron and C12 in Sec. 5
- mentioning of the Hubbard model and the extended Heisenberg model in Sec. 5
- comparison to the work by Jiang & Kivelson and resulting implications at the end of Sec. 5

### Submission & Refereeing History

Resubmission scipost_202011_00015v2 on 12 February 2021
Submission scipost_202011_00015v1 on 24 November 2020

## Reports on this Submission

### Report

The authors have answered all my comments in a satisfactory manner and have improved their manuscript so I recommend it for publication.

• validity: -
• significance: -
• originality: -
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### Report

All suggestions have been incorporated. Please accept manuscript.

• validity: top
• significance: high
• originality: high
• clarity: high
• formatting: excellent
• grammar: perfect