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}60 fullerene at half filling in the limit of strong on-site interaction UU. 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}20 or C_{32}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}20.
Highlights
We present the solution of the Heisenberg model on the C60 geometry
We observe that a good part of the angular momentum localizes on a 20-site ring along a “meridian” of the molecule. As this breaks the spatial symmetry, we conclude that the lowest Stot = 1 state is degenerate beyond the three components of the spin projection, i.e. has a multiplicity > 1 of its irreducible point group representation
We find that the symmetry-breaking 20-site ring is remarkably robust in our density-matrix renormalization group (DMRG) simulation and arises from different random starting states and for different site enumerations
Summary
The C60 buckminsterfullerene molecule, where 60 carbon atoms sit on the vertices of a truncated icosahedron, is a prominent molecule with a wealth of chemical and nanotechnological applications [1,2,3], and is of interest in terms of correlated-electron physics. Apart from trying to approximate the Hubbard model, a spin model on a fullerene-type geometry is interesting on its own, being connected to the problem of frustrated spin systems These arise on non-bipartite geometries like the triangular, kagomé or pyrochlore lattice, with building blocks of three-site clusters that cannot accommodate antiferromagnetic bonds in a commensurate fashion. Ih has 5 members within the Archimedean solids, of which the icosidodecahedron with 30 sites (triangular and pentagonal faces) has been the subject of intense study [27,28,29,30,31], since this is the geometry of the magnetic atoms in the Keplerate molecules {Mo72V30}, {Mo72Cr30} and {Mo72Fe30}, with S = 1/2, 3/2 and 5/2 respectively [32,33,34] It is solvable by exact diagonalization for S = 1/2 [27].
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