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

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.

Competition between frustration and spin dimensionality in the classical antiferromagnetic $n$-vector model with arbitrary $n$

“…What distinguishes fullerenes from Platonic and Archimedean solids is that their vertices are not equivalent, and as N increases so does the number of symmetrically unique vertices. On the other hand the icosahedral fullerenes are minimally frustrated, pointing to the importance of high symmetry for the magnetic properties, especially since they have also been found to behave nontrivially in a magnetic field both for classical and quantum spins [46,56,59,61]. This is also in agreement with the icosahedral and the four-dimensional Platonic solids forming MDGSs in a number of spin dimensions equal to their dimensionality in real space, which is also true for the icosahedral Archimedean solids.…”

Competition between magnetic frustration and spin dimensionality in the ground state of the classical antiferromagnetic $n$-vector model with arbitrary $n$

“…What distinguishes fullerenes from Platonic and Archimedean solids is that their sites are not equivalent, and as N increases so does the number of symmetrically unique vertices. On the other hand the icosahedral fullerenes are minimally frustrated, pointing to the importance of high symmetry for the magnetic properties, especially since they have also been found to behave nontrivially in a magnetic field both for classical and quantum spins [31,35,43,45]. This is also in agreement with the icosahedral and the four-dimensional Platonic solids forming ground states in a number of spin dimensions equal to their dimensionality in real space, which is also true for the icosahedral Archimedean solids.…”

Thermodynamics of the spin-half square-kagome lattice antiferromagnet

“…Bearing in mind the numerous studies of the lowenergy physics of the related kagome HAF we argue that our work may also stimulate other studies using alternative techniques, such as tensor network methods, DMRG, numerical linked cluster expansion or Green's function techniques [66][67][68][69][70].…”